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•-T'-       ••    —    .--  I   O 

v,  ..  ^  ;        .v  A"     -- « ^>5 


A    TREATISE 


PRINCIPLES    OF   CHEMISTRY. 


SonHon:   C.  J.  CLAY  AND  SONS, 

CAMBRIDGE   UNIVERSITY   PRESS   WAREHOUSE, 

AVE  MARIA  LANE. 


:   DEIGHTON,   BELL,   AND   CO. 

ILnpjtcj :   F.  A.  BROCKHAUS. 


A    TREATISE 


ON   THE 


PRINCIPLES    OF    CHEMISTRY 


M.    M.    PATTISON    MUIR,    M.A.,    F.R.S.E. 

FELLOW,    AND   PIUELECTOk   I:T   CHEMISTRY,   OF  GONVILLE  AND  CAIUS  COLLEGE, 
CAMBRIDGE. 


SECOND    EDITION. 


"In  nature  everything  is  distinct,  yet  nothing  defined  into  absolute 
independent  singleness."     WORDSWORTH. 


CAMBRIDGE: 

AT    THE    UNIVERSITY    PRESS. 
1889 

[All  Rights  reserved.  ] 


Cambridge : 

PRINTED   BY   C.   J.    CLAY,   M.A.   AND   SONS, 
AT  THE  UNIVERSITY   P^Go. 


4S-3 


If  in  this  book  I  have  shewn  any  just 
appreciation  of  the  scientific  study  of  nature, 
I  owe  it  to  the  teaching  of 

PROFESSOR  SIR  WILLIAM  THOMSON. 
To  him,  therefore,  I  dedicate  my  work. 


PREFACE. 


THIS  book  is  intended  to  give  a  fairly  complete  account 
of  the  present  state  of  knowledge  regarding  the  principles 
and  general  laws  of  chemistry. 

It  is  addressed  to  students  of  this  science  who  have 
already  a  considerable  acquaintance  with  descriptive  che- 
mistry, but  it  is  hoped  that  by  such  students  the  book  will 
be  found  complete  in  itself;  so  that  while  it  certainly  deals 
with  chemical  principles  and  theories  on  the  supposition  that 
its  readers  have  some  knowledge  of  chemical  facts,  yet  the 
book  may  fairly  claim  to  rank  as  a  systematic  treatise  on 
chemical  philosophy. 

While  I  have  tried  to  supply  full  information  regarding 
those  points  which  appear  to  me  of  most  importance,  I  have 
also  sought  to  avoid  great  detail,  and  to  present  a  sketch  of 
the  principles  of  chemistry  the  parts  of  which  shall  hang 
together  as  being  mutually  dependent. 

To  know  what  to  omit  has  been  one  of  the  most  difficult 
parts  of  my  undertaking.  The  chemical  student  is  too  often 
subjected  to  a  shower-bath  of  facts;  he  is  made  to  feel  that 


viii  PREFACE. 

'to  sit  as  a  passive  bucket  and  be  pumped  into... can  in  the 
long-run  be  exhilarating  to  no  creature.' 

An  attempt  is  made  in  this  book  to  treat  the  principal 
theories  of  modern  chemistry  to  some  extent  from  an  his- 
torical point  of  view,  and  to  trace  the  connexions  between 
the  older  theories  and  those  which  now  prevail  in  the  science. 
It  is  hoped  that  the  student  may  thus  gain  a  firmer  grasp  of 
those  theories  than  he  is  able  to  do  when  they  are  put  before 
him  as  entirely  creations  of  recent  times. 

I  have  tried  to  deal  with  chemical  facts  and  generalisa- 
tions so  as  to  shew  their  reality.  This  can  best  be  done, 
I  believe,  by  following  in  the  very  foot-prints  of  the  great 
discoverers,  by  watching  them  as  they  make  their  footing 
sure,  and  as  they  feel  their  way  up  the  heights.  That  the 
student  may  be  able  to  verify  the  accounts  I  have  given  of 
the  more  important  investigations,  and  more  especially  that 
he  may  fill  in  the  details  which  I  have  necessarily  omitted, 
I  have  given  copious  references  to  original  memoirs  and 
papers;  these  references  will,  I  believe,  be  found  correct,  at 
least  I  have  spared  no  pains  to  make  them  so.  I  have  also 
endeavoured  to  make  the  index  full  and  complete. 

So  far  as  I  am  aware,  no  sufficiently  comprehensive  guide 
to  the  study  of  the  principles  of  chemistry  exists,  in  an 
English  form,  although  we  have  many  excellent  works  dealing 
with  descriptive  chemistry,  with  the  materials,  that  is  to  say, 
from  which  chemical  science  is  being  constructed.  Professor 
Lothar  Meyer's  Die  modernen  Theorien  der  C/iemie,  to  a 
considerable  extent  meets  the  wants  of  the  German  student. 
I  have  made  free  use  of  that  book  in  preparing  my  own ;  but 
I  venture  to  think  I  have  incorporated  in  my  general  plan 
many  important  facts  and  principles  which  do  not  find  a 


PREFACE.  IX 

place  in  that  admirable  treatise.  I  have  also  regarded  the 
whole  subject  from  a  stand-point  somewhat  different  from 
that  occupied  by  the  German  Professor1. 

To  name  all  the  books  and  journals  from  which  I  have 
derived  assistance  would  be  tedious  and  absurd;  they  are 
sufficiently  indicated  in  the  notes  and  references2. 

I  have  tried  to  rest  every  important  statement  on  first- 
hand authority.  When  chemistry  is  regarded  from  the  point 
of  view  of  the  great  workers  therein,  it  wears  an  aspect 
very  different  from  that  with  which  it  confronts  the  mere 
text-book-taster. 

The  book  is  divided  into  two  parts.  The  first  part  is 
occupied  with  the  statement  and  discussion  of  the  atomic  and 
molecular  theory,  and  the  applications  thereof  to  such  sub- 
jects as  allotropy,  isomerism,  and  the  classification  of  elements 
and  compounds.  Somewhat  full  accounts  are  also  given,  in 
this  part,  of  thermal,  optical,  and  other  departments  of  physi- 
cal, chemistry,  in  so  far  as  the  results  and  methods  of  these 
branches  of  the  science  are  applicable  to  the  questions  re- 
garding the  composition  of  chemical  systems  which  are 
connoted  by  the  term  Chemical  Statics. 

The  second  part  of  the  book  is  devoted  to  the  subjects 
of  dissociation,  chemical  change  and  equilibrium,  chemical 
affinity,  and  the  relations  between  chemical  action  and  the 
distribution  of  the  energy  of  the  changing  system.  These, 
and  cognate  questions,  I  have  ventured  to  summarise  in  the 
expression  Chemical  Kinetics. 


1  An  English  edition  of  Modern  Theories  is  now  published. 

2  The  full  titles  of  the  various  journals  referred  to  are  given  on  pp.  xxii,  x> 


X  PREFACE. 

I  have  been  much  aided  in  my  task  by  my  friends 
Mr  C.  Slater1,  B.A.,  of  St  John's  College,  and  Mr  R.  Threlfall2, 
B.A.,  Scholar  of  Gonville  and  Caius  College.  The  former 
has  read  considerable  portions  of  the  proofs  and  has  made 
many  valuable  suggestions ;  the  latter  has  read  all,  except 
the  first  chapter  of  Book  I,  and  by  his  criticisms  and  remarks 
has  helped  me  to  make  many  important  points  much  clearer 
and  more  accurate  than  they  would  otherwise  have  been. 

M.  M.  PATTISON  MUIR. 

CAMBRIDGE,  October  1884. 


1  Now  Lecturer  in  Bacteriology  at  St  George's  Hospital.     - 

2  Now  Professor  of  Physics  in  the  University  of  Sydney. 


PREFACE    TO   THE    SECOND    EDITION. 


THE  aim  and  scope  of  the  book  have  not  been  changed. 
The  whole  has  been  thoroughly  revised,  and  Book  II  has 
been  entirely  rewritten.  The  revision  will,  I  hope,  make 
clearer  than  before  the  mutual  dependence  of  the  parts. 

Since  the  first  edition  was  published,  much  important 
work  has  been  done  on  subjects  treated  in  Book  I ;  the 
results  of  this  work  have  been  noticed  in  the  present  edition  ; 
at  the  same  time  some  chapters  have  been  shortened,  especially 
that  dealing  with  valency  and  isomerism  ;  the  arrangement 
of  these,  and  some  other,  chapters  has  been  altered.  The 
chapters  on  physical  methods  have  been  rewritten. 

When  the  first  edition  was  published,  the  study  of  chemical 
affinity  was  entering  on  a  new  phase  ;  since  1884  progress  has 
been  very  rapid,  and  to-day  we  are  much  nearer  the  goal  than 
we  were  five  years  ago.  The  great  importance  of  recent  work 
on  affinity  has  compelled  me  entirely  to  rewrite  Book  II.  In 
doing  this  I  have  largely  followed  Ostwald's  Lehrbuch  der 
allgemeinen  CJtemie ;  without  that  admirable  treatise,  the 
part  of  my  book  dealing  with  affinity  could  not  have  been 
written.  I  am  anxious  to  express,  as  strongly  and  warmly 


xii  PREFACE  TO   THE   SECOND   EDITION. 

as  I  can,  my  indebtedness  to  Prof.  Ostwald.  I  also  thank 
my  friend  Mr  Douglas  Carnegie,  M.A.  for  help  given  in 
revising  the  proofs  of  Book  II. 

'  As  this  edition  has  been  some  time  passing  through  the 
press,  and  as  the  progress  of  chemistry  has  been  very  rapid 
during  that  time,  the  lists  of  errata  and  addenda  are  fuller 
than  is  usual  in  a  book  of  this  character.  The  student  is 
requested  to  pay  attention  to  these  lists,  and  to  incorporate 
the  corrections  and  additions  in  the  text. 

M.  M.  P.  M. 

April  1889. 


TABLE   OF   CONTENTS. 


BOOK    I.     CHEMICAL   STATICS. 
CHAPTER   I.     ATOMS   AND    MOLECULES. 

Paragraph  Page 

If TRODUCTORY  I 

Beginnings  of  atomic  theory i  7 

Daltonian  conception  of  atoms 2,  3  8 

Volumetric  combination  of  elementary  gases    ) 

Law  of  Gay-Lussac \                                              4  I2 

Dalton's  criticism  of  this  law 5  12 

Avogadro's  generalisation     ........  6  13 

Wollaston's  equivalents 7  14 

Berzelius'  work  on  atomic  synthesis 8  16 

The  Berzelian  double  atom 9  19 

Dumas'  attempts  to  determine  molecular  and  atomic  weights         .  10  20 

Notation,  and  system,  of  Laurent  and  Gerhardt    ....  1 1  22 

The  atom,  the  molecule,  and  the  equivalent  differentiated      .  12  24 

The  molecular  theory  of  the  constitution  of  matter         ...  13  25 
Application  of  Avogadro's  law  to  determine  relative  weights  of 

elementary  molecules     ........  14  29 

Table  of  molecular  weights  of  elements 15  32 

Precautions  to  be  observed  in  determining  molecular  weights         .  16  34 

Correction  of  values  obtained        .......  17  35 

Deduction,  from  application  of  Avogadro's  law,  of  definition  of 

atomic  weight 18  37 

Table  of  data  for  finding  maximum  atomic  weights  of  elements     .  19  38 

Atomicity  of  elementary  molecules 20  45 

Formulae  of  liquid  and  solid  compounds 21  46 

Table  of  maximum  atomic  weights  of  elements      ....  22  48 

Law  of  Dulong  and  Petit 23  48 

Application  of  this  law,  in  modified  form,  to  compounds        .         .  24  50 

Data  concerning  atomic  heats  of  elements 25  51 

Indirect  determination  of  atomic  heats 26  54 

Discussion  of  law  of  Dulong  and  Petit 27  59 

M.  C.  b 


xiv  TABLE   OF   CONTENTS. 

Paragraph  Page 

Specific  heat  of  beryllium 28  61 

„  boron,  silicon,  and  carbon 29  63 

Limitations  to  application  of  law  of  Dulong  and  Petit  ...  30  66 
Comparison  of  law  of  Avogadro  with  that  of  Dulong  and  Petit  as 

aids  in  finding  values  of  atomic  weights  ....  31  67 

Mitscherlich's  law  of  isomorphism 32  69 

Groups  of  isomorphous  elements 33  72 

Application  of  this  law  to  determine  values  of  atomic  weights  .  34  74 

Raoult's  method  of  determining  molecular  weights  ...  35  76 

Chemical  methods  for  finding  molecular  and  atomic  weights  .  36  78 
Comparison  of  chemical  with  physical  methods  for  determining 

these  constants 37-85 

Table  of  atomic  weights,  with  summary  of  data  (and  references  to 

original  memoirs) 38  85 


CHAPTER  II.     ATOMIC   AND   MOLECULAR   SYSTEMS. 
SECTION  I.    NASCENT  ACTIONS. 

Examples  of  actions  called  nascent 39  96 

Explanation  of  these  actions  in  terms  of  the  molecular  theory  .  40  97 

Nascent  state  of  compounds 41  99 

Special  cases:  action  of  acids  on  metals 42  100 

Experimental  evidence  of  difference  between  actions  of  atsms  and 

molecules 43  106 

All  reacting  bodies  in  a  chemical  change  influence  that  change  .  44  107 
Should  the  expression  'nascent  action'  be  retained  in  chemical 

nomenclature? 45  109 

SECTION  II.    THE  DUALISTIC  AND  UNITARY  HYPOTHESES. 

Electro-chemical  investigations  of  Davy 46  1 1 1 

,,  ,,  Berzelius 47  113 

The  Berzelian  dualistic  hypothesis 48  115 

Dualistic  conception  of  acid  and  salt 49  116 

Faraday's  electrolytic  laws    .         .         .         .         .         .  .  50  117 

Reaction  against  dualism  led  by  Dumas,  Laurent,  and  Gerhardt    .  51  117 

Conception  of  compound  radicle  retained  by  the  new  school  .  52  119 

Classification  by  use  of  typical  substances 53  120 

SECTION  III.    EQUIVALENCY  OF  ATOMS. 

Conception  of  definite  substituting  value  applied  to  atoms  .  .  54  122 
Fundamental  data  for  determining  precise  meaning  of  terms 

monovalent,  divalent,  &c 55  124 

Application  of  these  terms  to  classification  of  atoms  of  elements    .  56  125 


TABLE   OF   CONTENTS.  XV 

Paragraph    Page 

Further  explanation  of  expression  valency  of  an  atom  .          .      57 — 59     129 — 132 
Consideration  of  possible  meanings  of  expressions  'bonds'  or  'units 

of  affinity '  as  applied  to  atoms 60 — 62     132 — 137 

General  considerations  regarding  valencies  of  atoms,  especially  as 
these  are  supposed  to  be  deduced  from  study  of  non-gasifiable 
compounds  ..........  63  137 


SECTION  IV.    ALLOTROPY  AND  ISOMERISM. 

The  molecule  considered  as  a  structure 64  138 

Differences  of  atomic  arrangements  are  connected  with  differences 

in  energies  of  molecules 65  139 

Two  kinds  of  variations  in  atomic  arrangement  possible          .         .  66  139 

Allotropy 67  141 

Polymerism 68  142 

Isomeric  and  metameric  molecules 69  1 43 

Formula  for  finding  maximum  number  of  monovalent  atoms  in  a 

molecule ;  saturated  and  unsaturated  molecules  ...  70  144 
Possible  isomerides  of  same  empirical  formula  .  .  .  .  71  145 
Formulae  of  molecules  which  cannot  exhibit  isomerism  .  .  72  146 
Illustrations  of  determinations  of  structural  formulae  .  .  .  73  146 
Atomic  groups  characteristic  of  classes  of  carbon  compounds  .  74  151 
Recapitulation  of  paragraphs  concerning  applications  of  hypo- 
thesis of  valency  75  154 

Generalisations  used  as  guides  in  finding  structural  formulae            .  76  156 

Illustrations  of  use  of  these  generalisations 77  156 

Further  application  of  hypothesis  of  valency  to  conception  of  the 

molecule  as  a  structure 78  162 

Functions  of  parts  of  a  molecule  are  dependent  on  nature  and  struc- 
ture of  the  whole  molecule     .......  79  162 

Illustrations  of  dependence  of  functions  of  parts  of  a  molecule  on 
the  nature  and  arrangement,  relatively  to  given  parts,  of  other 

atoms  in  the  molecule 80  163 

Illustrations  of  influence  exerted  on  the  function  of  one  atom,  or 
group  of  atoms,  by  the  arrangement  of  all  the  atoms  in  the 

molecule 81  165 

Chemical  stability  of  a  molecule  is  the  result  of  balance  between 

functions  of  various  parts  of  the  molecule        .         .         .         .  82  171 
Many  physical  properties  of  compounds  are  also  correlated  with 

such  molecular  balance 83,  84  172 

Thermal  data  connected  with  isomerism        ....      85 — 89     174 — 179 
General  considerations  regarding  relations  illustrated  in  pars.  85 

to  89 •                .         .  90  179 

Application  of  these  considerations  to  prevalent  views  on  valency  91  180 

Limitations  usually  placed  on  atomic  explanation  of  isomerism      .  92  181 

Geometrical  isomerism 93  182 

b2 


xvi  TABLE   OF   CONTENTS. 

Paragraph     Page 

Examples  of  use  of  hypothesis  of  geometrical  isomerism         .         .  94,95         185 

Summary  of  section  iv 96         191 

Appendix  to  section  IV 

Lossen's  criticism  of  the  various  meanings  assigned  to  term 

valency  ..........  193 

'  Are  the  carbon  bonds  of 'equal  value?' 198 


SECTION  V.    MOLECULAR  COMPOUNDS. 

Hypothesis  of  valency  not  strictly  applicable  to  phenomena  sug- 
gested by  terms  molecular  compounds  and  atomic  compounds  97  199 
Definition  of  molecular  compounds  impossible       ....  98  200 
Illustrations  of  phenomena   exhibited   by  bodies  classed   as   mo- 
lecular compounds 99  201 

Probable  existence  of  particles  more  complex  and  less  stable  than 

the  molecule 100  207 

Work  of  Lehmann  and  others  on  physical  isomerism     .         .         .  101  208 

No  fixed  boundary  between  molecular  and  atomic  compounds        .  102  218 

The  physical  and  the  chemical  conception  of  the  molecule     .         .  103  219 


CHAPTER  III.     THE   PERIODIC   LAW. 

Earlier   investigations  into   connexions  between   atomic  weights 

and  properties  of  elements 104         222 

Statement  of  the  periodic  law        .......         105         223 

Illustrations  of  periodic  connexion  between  atomic  weights  and 

properties  of  elements     .         .         .         .         .         .         .         .         106         224 

Relations  between  atomic  weights  and  atomic  volumes  .         .         107         224 

„  ,,  „  and  fusibilities  of  elements        .         108         228 

,,  ,,  ,,  and  various  physical  constants 

of  elements    ..........         109        229 

Illustrations  of  applications  of  periodic  law  : 

(1)  to  predict  properties  of  unknown  elements        .         .         .         no         230 

(2)  to  guide  the  study  of  properties  of  similar  elements  .         in         232 
'  Odd  series' ,  'even  series',  '  long  periods'1 ,  and  '  typical  elemeitts'     .         112         235 
Connexions  between  general  formulae  of  classes  of  compounds  and 

atomic  weights  of  elements  in  these  compounds  .  .  .  113  239 
Valency  considered  as  a  periodic  function  of  atomic  weights  of  the 

elements .  114  241 

General  remarks  on  the  periodic  law  applied  to  classification  .  115  243 


TABLE   OF   CONTENTS. 


CHAPTER  IV.    APPLICATIONS  OF  PHYSICAL  METHODS 
TO   QUESTIONS   OF   CHEMICAL  STATICS. 

Paragraph  Page 

Introductory 116  246 

SECTION  I.    THERMAL  METHODS. 

Introductory 117  247 

Notation  used  in  thermal  chemistry 118  248 

Endothermic  and  exothermic  reactions           .         .         .         .         .  119  252 

Calculation  of  thermal  values  of  chemical  changes         .         .         .  120  254 
Illustrations  of  connexion  between  chemical  changes  and  changes 

of  energy 121  259 

A  chemical  change  consists  of  at  least  two  parts    .         .        .         .  122  262 

Attempts  to  determine  thermal  values  of  molecular  decompositions  123  263 
Thermal  results  applied : 

(1)  to  reactions  between  metals  and  acids       .         .        .        .  124  264 

(2)  to  allotropy      .        .        .        ."....        .        .        .  125  266 

(3)  to  classification  of  elements 126  266 

(4)  to  classification  of  compounds 127  267 

(5)  to  neutralisation  of  acids  by  bases,  and  of  bases  by  acids  .  128  269 
Connexions  between  thermal  and  material  changes  occurring  in 

same  chemical  system 129  274 

Influence  of  temperature  on  thermal  value  of  a  chemical  change   .  130  275 
Influence  of  masses  of  reacting  bodies  on  thermal  value  of  a  chemi- 
cal change 131  276 

Thermal  value  of  a  chemical  reaction  is  the  sum  of  several  partial 

values 132  277 

The  law  of  maximum  work  .         .         .         .         .         .         .         .  133  278 

Illustrations  of  application  of  thermal  methods  to  determine  struc- 
tural formulae 134  282 

Connexions  between  boiling  points  and  composition  of  hydro- 
carbons    135  286 

Concluding  remarks  to  this  section 136  289 

SECTION  II.    OPTICAL  METHODS. 

Statement  of  methods  to  be  considered  in  this  section   .         .        .  137  289 

Formulae  for  calculating  the  refraction-equivalent  of  a  carbon 

compound  .  .  .  .  .  .  .  .  .  .  138  289 

Is  the  value  to  be  assigned  to  the  refraction-equivalent  of  an  ele- 
ment constant  in  all  liquid  compounds  of  that  element?  .  139  291 

Method  of  calculating  atomic  refraction  from  determinations  of 

molecular  refractions  of  compounds 140  291 


xviii  TABLE  OF   CONTENTS. 

Paragraph    Page 

Connexions  between  molecular  refraction  and  isomerism        .         .         141         292 
Applications  of  connexions  examined  in  preceding  paragraph         142,  143         295 

Specific  rotatory  powers  of  substances 144         299 

Rotatory  power  depends  on  atomic  composition  of  molecules,  but 
is  also  modified  by  reactions  between  optically  active  and  in- 
active molecules 145  303 

van't  HofFs  hypothesis  regarding  connexions  between  molecular 

structure  and  specific  rotatory  power 146         304 

Illustrations  of  modifying  influence  exerted  by  optically  inactive 

substances  on  rotatory  power  of  optically  active  compounds  .  147  309 
Magnetic  rotatory  powers  of  liquid  compounds  .  .  .  .  148  311 
Connexions  between  absorption-spectra  and  structure  of  molecules 

of  carbon  compounds 149         314 


SECTION  III.    METHODS  BASED  ON  DETERMINATIONS  OF  THE 
MOLECULAR  VOLUMES  OF  COMPOUNDS. 

Explanation  of  constant  considered  in  this  section  .  .  .  1 50  317 
Data  to  illustrate  connexions  between  molecular  volumes  and 

composition  of  compounds 151  319 

Data  to  illustrate  connexions  between  molecular  volumes  and 

actual  valencies  of  atoms  in  given  molecules  .  .  .  .  152  320 
Data  to  illustrate  connexions  between  molecular  volumes  and 

distribution  of  interatomic  actions  .  .....  153 — 4  321 

Molecular  volumes  of  solid  compounds 155  325 

Discussion  of  meaning  of  molecular  volume  .  .  .  .  156  32  J 


SECTION  IV.    METHOD  BASED  ON  'ETHERIFICATION-VALUES'. 

Statement  of    method,    and   illustrations   of  application   of  this 

method 157         331 

SECTION  V.    MISCELLANEOUS  METHODS. 

Capillarity-constants 158         335 

Transpiration-rates 159         336 

Electrolysis 1 60         336 

Concluding  Remark*  to  Book  1 161         338 


BOOK    II.     CHEMICAL    KINETICS. 


CHAPTER   I.     THE   LAW   OF   MASS-ACTION. 


Paragraph  Page 

Introductory  remarks  on  subject  of  this  Book         ....  162  339 

Early  history  of  term  affinity         .......  163  340 

Bergmann's  tables  of  affinity 164  340 

Berthollet's  Essai  de  Statique  Chimique 165  341 

Bergmann's  and  Berthollet's  views  on  affinity  contrasted        .         .  166  345 

Experiments  on  influence  of  mass 167  346 

Guldberg  and  Waage's  law  of  mass-action 168  347 

Equation  of  equilibrium  arrived  at  without  using  notion  of  chemical 

force 169  3^p 

Experimental  verifications  of  equation  of  equilibrium    .         .         .  170,171  351 


CHAPTER   II.     CHEMICAL   DYNAMICS. 

Methods  of  measuring  chemical  forces 172  355 

SECTION  I.    VELOCITY  OF  CHEMICAL  CHANGE. 

Equation  for  representing  reaction-velocity 173,  174  356 

Amount  of  change  proportional  to  mass  of  changing  body    .         .  175  357 

Cases  where  several  bodies  undergo  change  simultaneously  .         .  176  359 

Principle  of  coexistence  of  reactions 177  361 

Case  of  a  solid  reacting  with  a  liquid 1 78  362 

SECTION  II.    CHEMICAL  EQUILIBRIUM. 

General  sketch  of  methods 179  363 

System  of  two  changing  bodies 180  363 

System  of  four  changing  bodies 181,182  367 

Thomsen's  experiments  on  partition  of  a  base  between  two  acids  .  183  368 

Ostwald's  experiments  on  the  same  subject 184  372 

Etherification  of  alcohols 185  374 


XX  TABLE   OF   CONTENTS. 

Paragraph    Page 

Equilibrium  of  physically  heterogeneous  systems  .  .  .  .  186  374 
Summary  of  law  of  mass-action  and  principle  of  coexistence  of 

reactions 187  378 

SECTION  III.    THERMODYNAMICAL  METHODS  APPLIED  TO  CHEMICAL 
EQUILIBRIUM. 

Horstmann's  condition  of  equilibrium 188  379 

Gibbs'                   „                   „               ......  189  380 

von  Helmholtz's_/9-w  and  bound  energy          .....  190  382 

Berthelot's  law  of  maximum  work 191  383 

SECTION  IV.    MOLECULAR  METHODS  APPLIED  TO  CHEMICAL 
EQUILIBRIUM. 

Williamson's  hypothesis 192  385 

Guldberg  and  Waage's  treatment  of  the  subject     ....  193  386 

Application  of  vortex-atom  theory  by  J.  J.  Thomson     .         .         .  194  387 

SECTION  V.    DISSOCIATION. 

Instances  of  dissociation 195  389 

So  called  abnormal  vapour-densities 196  391 

Equilibrium-pressure  in  dissociation-processes  ....  197  392 
Dissociation  of  ammonium  chloride  compared  with  that  of 

hydrogen  iodide 198  392 

Dissociation  of  a  solid  into  a  solid  and  a  gas  .  .  .  .  199  394 

Dissociation  when  several  compounds  may  exist  together  .  .  200,  201  394 
Absorption  of  gases  by  solids  contrasted  with  combination  of 

gases  with  solids 202  398 

Application  to  dissociation  of  equations  of  equilibrium  .  .  203  398 

Thermodynamical  aspects  of  dissociation 204  401 

Molecular  ,,  ,,  205,  206  402 

Dissociation  may  be  due  to  molecular  collisions  or  to  action  of 

external  agencies 207  405 

Summary  of  Chapters  I.  and  II.  of  this  Book  ....  208  405 


CHAPTER  III.     CHEMICAL  AFFINITY. 

Retrospect 209  407 

Coefficients  of  affinity  arrived  at  by  using  Guldberg  and  Waage's 

equation  of  equilibrium 210  408 

SECTION  I.    SPECIFIC  AFFINITY-COEFFICIENTS  OF  ACIDS  AND  BASES. 

Statement  of  equation  of  equilibrium  in  suitable  form   .         .         .         211  409 

Thomsen's  method  of  finding  affinities  of  acids      ....         212  410 


TABLE   OF   CONTENTS.  xxi 

Paragraph  Page 
Ostwald's  examination  of  the  constancy  of  the  affinity  of  an  acid 

or  base  .  .  .  .  .  .  .  .  .  .  213  412 

The  same  subject  continued 214-220415-422 

There  is  a  definite  connexion  between  electrical  conductivities  of 

acids  in  solution  and  the  velocity-constants  of  the  changes 

brought  about  by  these  acids  .  .  .  .  .  .221  422 

Molecular  conductivity  of  an  acid  defined 222  424 

Law  of  dilution  for  monobasic  acids 223  424 

Affinities  of  monobasic  acids  connected  with  relative  conductivities 

stated  in  terms  of  maximum  conductivities  ....  224  427 

The  law  of  Kohlrausch 225  428 

Method  for  finding  maximum  conductivity  of  a  monobasic  acid  .  226  431 

Conductivities  of  polybasic  acids 227  432 

Conductivities  of  bases 228  435 

Determination  of  affinity  of  a  monobasic  acid  from  measurements 

of  conductivity  of  its  aqueous  solution 229  436 

SECTION  II.    CONNEXIONS  BETWEEN  THE  AFFINITY-COEFFICIENTS 
AND  THE  CONSTITUTION  OF  ACIDS. 

Statement  of  method  for  finding  affinity-coefficients        .         .         .         230  439 

Examples      .         .         .    - 231  440 

Dibasic  acids         ..........         232  443 

General  remarks  on  results  obtained      ......         233  446 


SECTION  III.    CHEMICAL  CHANGE. 

Recapitulation  of  former  paragraphs  bearing  on  this  subject .         .  234  450 

van't  Hoff's  law  of  osmotic  pressure 235  450 

Planck's  work  in  the  same  direction 236  454 

Arrhenius'  development  of  the  law  of  van't  Hoff  ....  237  454 

Additive  and  cumulative  properties 238  456 

Ostwald's  examination  of  the  hypothesis  of  electrolytic  dissociation  239  457 

Summary  of  preceding  paragraphs        ......  240  460 

Hypothesis  of  chemical  change  occurring  between  electrolytes       .  241  460 

Limitations  applied  to  this  hypothesis 242  464 

Action  of  the  solvent  on  the  dissolved  electrolyte ....  243  465 

Instances  of  chemical  changes  which  occur  only  in  presence  of 

water    ...........  244  466 

Constitutive  properties  ........  245  468 

Affinity  and  valency 246  469 

Affinity  and  energy-changes .         .......  247  471 

Energy-changes  and  electromotive  force 248  473 

Concluding  remarks 249  475 


TITLES   OF  JOURNALS   CONTAINING    MEMOIRS   TO 
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ABBREVIATED  TITLES. 

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Proc.  R.  I. 


Amer.  Chem.  Journal. 

I  Amer.  Journ.  of  Set.  a 
or  1     Arts 

Amer.  Journal. 


lAmet 
J     Af 

(Sill. 


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andSci. 
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Pogg.  Ann. 
Wied.  Ann. 


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,,     series  2,  15  vols.  (1863-1877). 
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separately,    from    1878   to   present  time.     The 
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quently quoted  in  memoirs,  &c.,  as  Ann.  Phys. 
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TITLES   OF  JOURNALS   OF   REFERENCE. 


XXlll 


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Berlin. 
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Publication  discontinued.] 

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und  Verwandtschaftslehre ;  herausgegeben  von 
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wards.] 

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1873-1881.] 

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onwards.] 

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Gazetla  chimica  italiana. 


ERRATA. 


The  Student  is  advised  to  insert  the  following  corrections  in  their  proper  places 
in  the  text. 


28.     Note  i;  for  'Chap.  III.'  read  'Chap.  II.  sections  4  and  5'. 

33.  Dele  nos.  1 1  and  1 2  in  table. 

„      Note  i;  for  '1888'  read  '14.  410'. 

34.  Note  i;  for  '1888'  read  '14.  410'. 

,,  Notes  n  and  12;  dele,  and  substitute  'Biltz  (Zeitschr.  fur  physikal.  Ckemie, 
2.  920)  shews  that  the  molecular  weight  of  sulphur  gas  is  represented 
only  by  the  formula  S2'. 

38.     Fourth  line  from  top ;  for  'the  weight  of of  hydrogen'  read  'twice 

the  specific  gravity  of  a  gas  referred  to  hydrogen  as  unity'. 

42.  Fourth  line  from  bottom;  for  '257*0'  (in  fourth  column)  read  '254-84', 

and/or  '193'  (in  fifth  column)  read  '191'. 

43.  Line  5    from  bottom;    in  place  of  data   for  ferric  chloride  insert  '5'  15  | 

i48'68  |  i62'oi  |  55'9  iron+io6'ii  chlorine'. 

44.  Note  5;  for  '1887'  read  '14.  410'. 

„      Note  6;  dele  and  insert  'Biltz  and  Meyer,  Zeitschr.  fur  physikal.  Chemie, 

2.  184'. 
„      Note  12;  dele  and  insert  'Griinewald  and  V.  Meyer,  Ber.  21.  687'. 

45.  Table;  dele  last  column. 

48.     Table;  for  '[Iron  ni'8]'  read  'Iron  55'9',  and  for  '[Gallium   138]'  read 

'Gallium  69-9'. 

,,       Table;  for  'Osmium  i93(?)'  read  'Osmium  191'. 
,,      Note  i;  dele. 

„      Note  i;for  'elements'  read  'element'. 
53.     Bottom  line ;  for  'in'  read  'on'. 

60.  Second  line  from  top ;  for  '  omitting  the  three  elements  which  are  placed 
in  brackets  in  the  former  table,  of  the  43  elements'  read  'omitting  the 
element  which  is  placed  in  brackets  in  the  former  table,  of  the  45 
elements'. 

,,      Fourteenth  line  from  top;  for  'there  are  three  elements viz.  iron, 

copper,  and  gallium'    read    'there  is  one  element viz.  copper'; 

and  make  the  necessary  corrections  in  other  parts  of  this  page. 
71.     Sixth  line  from  bottom ;  for  'form'  read  'forms'. 
88.     Third  line  from  top  of  table,  second  column ;  for  '  Fe2Cl6' 

read  'FeCl3'.  \    See  Addenda. 

,,  fifth  column;  dele  '[see  p.  60]'. 


ERRATA.  XXV 

PAGE 

91.     Second  line  from  bottom  of  table;  for  '193'  read  'igi';for  '48-25'  read 
'4775';    afier   'Osmium  tetroxide'  add   'Potassium-osmium  chloride'; 
dele  note  in  column  VIH.  referring  to  osmium;  transpose  data  regarding 
osmium  so  as  to  come  above  data  for  iridium.     See  Addenda. 
99.     Note  carried  on  from  p.  98 ;  dele  last  two  lines  of  this  note. 
in.     Note;  dele  this  note. 

126.     Note;  dele  'determinations  of  the  spec,  gravity this  question'  and 

insert  'According  to  Thorpe  and  Hambly  (C.  S.  Journal,  B5.  163)  there 
is  no  evidence  for  the  separate  existence  of  a  definite  gaseous  molecule 
of  hydrogen  fluoride  other  than  HF'. 
128.     Line  12  from  bottom  ;  for  '37'  read  '39'         l 
„        Line  it  from  bottom ;  for  'six'  read  'nine'     j     k 

130.  Line  1 8  from  bottom;  for  'six'  read  'nine',  and  for  '37'  read  '39'. 

131.  Line  12  from  bottom;  for  '37'  read  '39'. 

141.     Line  13  from  top;  for  'six'  read  'five',  and  dele  'sulphur'. 
,,        Line  18  from  top;  dele  from  'the  molecule  of  sulphur'  to  '2  atoms'. 
,,        Line  6  from  bottom;  dele  from  'of  the  hexatomic'  to  'of  sulphur'. 
143.     Line  13  from  bottom;  dele  from  'another  instance'  to  'SnCl2'. 
1 86.     Line  2  from  bottom;  for  'carbonation'  read  'carbon  atom'. 
210.     Line  10  from  bottom ;  for  '195'  read  '195°'. 
225.     Table,  Group  fn  ;  for  'Ga  =  69'  read  'Ga  =  7o'. 

,,         ,,     vni ;  for  (Os=i93(?)'  read  '05=191',  and  transpose  Os  and 
Ir,  putting  Os  before  Ir. 

229.  Line  15  from  top;  for  '585'  read  '585°'. 

230.  Line  1 4  from  bottom  ;  for  '69'  read  '70'. 

231.  Line  2  from  top  ;  for  '69'  read  '69'9'. 

236.     Table,  Group  ill;  for  'Ga=69'  read  'Ga=7o'. 

,,         ,,     vni ;  for  '05=193'  read  '  05=191',  and  place  Os  before  Ir. 
292.     Line  8  from  bottom;  paragraphing  wrong,  for  '41'  raz</'141'. 
309.     Note  3;  for  '  Journal''  read  'ZeitscAr'. 

k'  k' 

352.     In  the  equation  ;forl(p-  *)  =  j  (/  +  •*)'  read  '(/>—  x)=  j  (P'  +  x)'. 

355.     Line  8  from  bottom ;  for  'constant'  read  'coefficient'. 

359.     Line  3  from  top;  for  'cases  where  more  than  one  body  undergoes'  read 

'cases  where  limited  quantities  of  more  than  one  body  undergo'. 
361.     Line  5  from  top;  for  'if  A  =  FeSO4  and  B  =  KC1O3'   read  'if   A  =  the 

quantity  of  potassium  chlorate  and  B  =  the  quantity  of  ferrous  sulphate'. 

364.  Line  1 1  from  top  ;  for  '  obtained '  read  '  attained '. 

,,       Line  14  from  bottom;  dele  'and  as  these  masses  are  independent  of  the 
original  values  of/  and/". 

365.  Line  1 6  from  bottom;  dele  'constancy  of  the'. 

367.  Line  13  from  top;  after  'and  therefore'  insert  'by  the  same  reasoning'. 

371.  Line  5  from  top;  dele  'and  £ '. 

372.  Lines  9  and  10  from  bottom;  for  'increase'  read  'decrease'. 

373.  Line  17  from  bottom ;  for  'greater'  read  'smaller'. 

,,        Line  15  from  bottom ;  for  'increase'  read  'decrease'. 

376.     Line  15  from  top;  for  'a  constant  temperature'   read  'constant  temper- 
atures'. 


ADDENDA. 


The  Student  is  advised  to  insert  the  following  additions  in  their  proper  places 
in  the  text. 

PAGE 

34.     Line  3  from  top;   add  'Biltz  and  Meyer  (Ber.  22.   725)  have  vaporised 
arsenic,  antimony,  bismuth,  phosphorus,  and  thallium,  at  about  1700°; 
the  vapour  densities  point  to  the  molecular  formulae  As,,  Sb,,  Bi,  ?P2, 
T12.     These  results  are  not  regarded  as  final  by  Biltz  and  Meyer'. 
39 — 43.     Insert  in  table ; 

'3b  Tellurium   diethide  6-47     i86'8     182*88     125    tellurium +  47-88    carbon 

+  10  hydrogen'. 
<3c  Bismuth  triethide       9*1       262-2     252-91     208   bismuth   +35-91    carbon 

+  9  hydrogen '. 

1 12»  Ferrous  chloride        4-31     124-43  127-64       55-9  iron      +71-74  chlorine'. 
44.     Note  i ;  add  'See  also  Thorpe  and  Hambly  C.  S.  Journal,  55.  163'. 
Insert  Note;  '3b  and  3°.     Marquardt,  Ber.  21.  2035'. 

Note  ii ;  in  loth  line  of  note  insert  'see  also  Roux  and  Louise,  Compt.  rend. 
106.  73;  also  Quincke,  Zeit.  fiir  physikal.  Chemie,  3.  164.  For  a  col- 
lection of  data  bearing  on  vapour  densities  of  the  chlorides  of  Al  and 
allied  metals,  see  Young,  Nature,  39.  198'. 

Insert  note;  '  12".     Nilson  and  Pettersson,  C.  S.  Journal,  53.  827'. 
Note  13;  at  end  of  note  add  'See  also  Nilson  and  Pettersson,  C.  S.  Journal, 

53.  822'. 

76.  Note;  add  '  For  practical  methods  of  applying  Raoult's  law  see  (among 
others)  Hentschel  Zeitschr.  fur  physikal.  Chemie,  2.  306;  Beckmann, 
ibid.  2.  638,  Eykman,  ibid.  2.  964  '. 

83.     Note  ;  add  '  The  example  given  in  the  text  is  not  a  good  one,  as  the  existence 
of  any  definite  gaseous  molecules  of  ferric  and  ferrous  chloride  except 
FeCl3  and  FeCl2  is  very  doubtful;  see  p.  44'. 
88.     First  line  of  table,  second  column;  <M&/'?CrQ2'. 

Eighth  line  of  table,  second  column;  add  'GaCI3,  GaCl2'. 
90.     Sixth  line  of  table,  second  column  ;  add  '  InCU,  ?  InCl  . 
95.     Reference  to  Os;  #</</' Seubert,  Ber.  21.  1839'. 

Reference  to  Pt ;  add  '  (See  also  Seubert,  Ber.  21.  2179)  '• 


ADDENDA.  XXV11 

PAGE 

127.  To  list  of  monovalent  atoms  ;  add  '  ?  In '. 

To  list  of  divalent  atoms  ;  add  '  In,  Ga,  Fe,  ?  Cr '. 
To  list  of  trivalent  atoms ;  add '  Fe,  Ga '. 

To  list  of  data  on  lower  part  of  page;  add  'PInCI,  InCl2,  FeClj,  FeCl3, 
GaCl2,  GaCl3,?CrCl2'. 

128.  Line  7  from- bottom;  insert  '  the  atoms  of  gallium,  iron,  and  indium,  and 

probably  also  the  atom  of  chromium,  are  divalent  and  trivalent'. 

229.  Note  5;  add  to  this  note,  '  But  de  Boisbaudran  has  calculated  the  atomic 
weights  of  gallium  and  germanium  from  considerations  based  on  the 
relations  between  the  atomic  weights,  and  the  wave-lengths  of  the  chief 
lines  in  the  spectra,  of  similar  elements.  (See  articles  Gallium  and 
Germanium  in  the  new  edition  of  Watts'  Dictionary  of  Chemistry, 
vol.  ii.)'. 

267.     Note;  add  to  this  note  'The  following  data  for  solid  mercury  compounds 
are  given  by  Nernst  (Zeitschr.  filr  physikal.  Chemie,  2.  23). 
[Hg,  0*1  =  53,200  [Hg,  ^  =  40,5000  [Hg,  I2]  =  24,300). 

298.  Note  6;  add  '  See  also  Conrady,  Zeitschr.  fur  physikal.  Chemie,  3.  210'. 

299.  Note;    add  'Weegman   (Zeitschr.  filr  physikal.   Chemie,   2.  218,258)  has 

conducted  a  series  of  very  careful  measurements  of  R  for  chloro-  and 
bromo-derivatives  of  hydrocarbons;  his  results  on  the  whole  confirm 
those  of  Briihl ;  they  also  emphasise  the  need  of  further  researches'. 

311.     Notey,  <*/</'1888.  561'. 

317.  Note  2;  to  list  of  memoirs  add  'An  historical  sketch,  by  Kopp,  of  the 
position  of  our  knowledge  of  the  molecular  volumes  of  liquid  compounds 
is  to  be  found  in  Anna  If  n,  250.  i  [1889]'. 


"  L'action  chimique  est  reciproque :  son  effet  est  le  resultat  d'une  tendance 
mutuelle  a  la  combinaison ;  on  ne  peut  pas,  a  la  rigeur,  dire  plutot  qu'un  liquide 
agit  sur  un  solide,  qu'on  ne  peut  dire  que  le  solide  agit  sur  le  liquide :  la 
commodite  de  1 'expression  fait  transporter  sans  inconvenient  toute  1'action  dans 
1'une  des  deux  substances,  quand  on  veut  examiner  1'effet  de  cette  action  plutot 
que  1'action  elle-meme."  BERTHOLLET. 


I 

LOS  ANQELJLS,  -:-  CAL. 


INTRODUCTORY. 


CHEMISTRY  is  preeminently  the  science  which  concerns 
itself  with  the  changes  presented  in  material  phenomena;  it 
is  the  science  which  attempts  to  classify  the  mutations  that 
matter  undergoes. 

In  the  chemical  examination  of  any  kind  of  matter  two 
questions  have  always  pressed  for  answers: — What  can  this 
substance  do?  Of  what  is  this  substance  composed?  While 
attempting  to  answer  these  questions  separately,  and  while 
thus  more  or  less  adopting  two  schemes  of  classification, 
chemists  have  for  the  most  part  recognised  that  no  complete 
answer  could  be  given  to  either  question  considered  wholly 
apart  from  the  other;  hence  the  two  methods  of  chemical 
investigation,  and  the  two  lines  of  chemical  advance,  have 
generally  been  closely  interwoven. 

In  older  times  a  substance  was  said  to  be  capable  of 
doing  this  or  that  because  it  contained  certain  elements  or 
essences ;  substances  were  classed  together  because  of  simi- 
larity of  actions,  but  the  points  of  resemblance  on  which 
classification  was  based  were  uncertain  and  undefined:  the 
conception  of  element  was  paramount.  The  substances  in 
a  class  shewed  many  or  a  few  points  of  resemblance  because 
each  member  of  the  class  contained  the  same  element,  and 
vhence  was  a  more  or  less  perfect  means  for  exhibiting  the 
properties  of  that  element-  The  ideas  of  composition  and 
properties,  as  we  now  use  these  expressions,  were  both  im- 
plied in  the  older  conception  of  element. 

M,  C.  I 


2  INTRODUCTORY. 

If  it  be  granted  that  the  various  forms  of  matter  are 
vehicles  for  displaying  the  properties  of  a  few  elements,  it 
follows  that  the  addition  or  withdrawal  of  this  or  that  ele- 
ment will  probably  suffice  to  change  one  into  another  form 
of  matter.  Hence  arose  the  art  of  alchemy  and  the  pursuit 
of  the  philosopher's  stone.  This  pursuit  resulted  in  the  ac- 
cumulation of  many  facts  most  of  which  could  for  some  time 
be  explained  by  aid  of  the  one  underlying  general  concep- 
tion of  element.  But  as  facts  accumulated  the  foundation 
was  found  to  be  too  narrow  to  bear  the  structure  raised  upon 
it;  a  need  was  felt  for  minor  explanations  and  for  partial 
hypotheses.  Observers  began  to  contrast  sour,  acid,  sub- 
stances, with  mild,  tasteless,  non-corrosive,  substances;  hence 
arose  the  division  of  a  large  class  of  bodies  into  two  minor 
classes,  acids  and  alkalis.  This  classification  when  carried 
to  completion  produced  the  school  of  tatro-chemists,  in 
whose  hands  chemical  science  became  a  branch  of  the  art 
of  medicine.  But  once  again  facts  were  observed  which 
could  not  be  explained  by  the  theories  of  the  medical 
chemists:  the  experimental  method  was  recognised  as  alone 
leading  to  definite  and  trustworthy  results  in  the  examination 
of  natural  phenomena;  but  the  experimental  method,  it  was 
found,  to  be  of  value  must  be  accurate,  and  to  be  accurate 
must  be  quantitative.  Advance  became  rapid.  The  con- 
ception of  element  remained,  but  in  modified  form ;  the  dis- 
tinction between  alkali  and  acid  remained,  but  proved  to 
mean  at  once  less  and  more  than  its  originators  supposed. 
Bodies  were  compared  as  to  their  actions  and  as  to  their 
composition  ;  the  comparison  led  on  the  one  hand  to  the 
recognition  of  force  exerted  by  one  body  on  another,  called 
affinity,  and  on  the  other  hand  to  the  recognition  of  ultimate 
forms  of  matter,  called  elements,  of  which  all  bodies  are  com- 
posed. 

From  this  point  the  two  broad  paths  of  advance  become 
more  easily  distinguished ;  advance  is  made  by  seeking  answers 
to  questions  such  as  these : — What  is  the  nature  of  the  ele- 
ments ?  What  is  the  composition  of  compounds  ?  Can  the 
facts  regarding  elementary  combinations  be  generalised  ? 


INTRODUCTORY.  3 

Advance  is  also  made  .by  pursuing  inquiries  indicated  by 
such  questions  as  these : — What  connexion,  if  any,  exists 
between  the  properties  of  elements  and  of  compounds  of  these 
elements  ?  What  actions  are  these  compounds  capable  of 
performing?  And  advance  is  also  made  by  combining  both 
methods  of  inquiry  in  seeking  answers  to  such  a  question  as 
this: — Why  are  the  properties  of  these  compounds  such  as 
they  are  observed  to  be? 

At  one  time  those  chemists  for  whom  the  composition  of 
compounds  was  all-important  have  been  supreme;  at  another 
time  the  place  of  authority  has  been  occupied  by  those  who 
regarded  function,  or  power  of  doing,  as  the  essential  subject 
of  study.  The  greatest  outcome  of  the  work  of  the  former 
school  is  the  atomic  hypothesis,  now  merged  in  the  wider 
molecular  and  atomic  theory;  the  most  important  result  of 
the  studies  of  the  latter  school  is  the  conception  of  chemical 
affinity ;  both  have  taken  part  in  the  development  of  the 
modern  views  regarding  molecular  structure  and  rational 
formulas. 

While  assigning  the  credit  of  special  advances  to  one  of 
the  two  great  schools  of  chemistry,  we  cannot  but  recog- 
nise that  these  advances  have  been  made  by  the  help  of 
suggestions  borrowed  from  the  other:  recent  developments 
of  the  atomic  theory  cannot  be  separated  from  the  rise  of  the 
unitary  system ;  the  latest  hypotheses  regarding  the  structure  of 
molecules  are  connected  with  the  subject  of  chemical  affinity. 

Eighty  years  ago  Berthollet  attempted  to  arrange  the 
facts  of  chemical  action  under  a  general  conception  which 
should  serve  to  connect  chemical  with  physical  changes;  but 
the  attempt  was  only  partially  successful  because  of  the  scanty 
supply  of  purely  chemical  data.  General  views  of  chemical 
action  were  soon  abandoned  for  a  study  of  the  properties  of 
the  products  of  this  action ;  but  of  late  years  many  chemists 
have  resumed  the  investigation  of  the  general  conditions  of 
chemical  action,  and  have  obtained  results  which  give  good 
grounds  for  hoping  that  this  study  will  throw  light  on  the 
masses  of  facts  already  accumulated  concerning  compounds, 
and  groups  of  compounds,  and,  taken  along  with  that  method 

I — 2 


4  INTRODUCTORY. 

of  investigation  which  is  based  on  a  study  of  the  composition 
of  compounds,  will  lead  to  the  establishment  of  chemistry  as 
a  branch  of  the  science  of  physical  dynamics. 

The  study  of  the  motions  of  material  bodies  considered  as 
accompanying  mutual  actions  between  these  bodies  belongs 
to  the  general  science  of  dynamics.  Phenomena  presented 
by  mutually  acting  bodies  wherein  the  properties  of  these 
bodies  are  not  permanently  modified  belong  to  the  domain  of 
physical  science.  Chemistry  deals  with  those  reactions 
between  elements  and  compounds  wherein  permanent  modifi- 
cations in  the  properties  of  the  bodies  occur.  Or,  we  may 
say  that  whereas  physical  science  is  concerned  with  the  pro- 
perties of  this  or  that  kind  of  matter  considered  for  the  most 
part  apart  from  the  action  on  it  of  other  kinds  of  matter, 
chemistry  is  concerned  with  the  mutual  actions  which  occur 
between  matter  of  different  but  definite  kinds  whereby  per- 
sistent changes  in  the  properties  of  the  reacting  kinds  of 
matter  occur. 

Chemistry  furnishes  problems  for  the  solution  of  which 
physical  and  dynamical  methods  are  applicable.  Chemical 
science  is  ever  tending  toward  abstract  truths,  i.e.  truths 
involved  in  many  phenomena  although  actually  seen  in  none: 
but  before  she  gains  abstract  truths  chemistry  amasses  many 
general  truths,  i.e.  'truths  which  sum  up  many  facts.'1 

The  chemist  is  set  to  solve  the  problem  : — Why  are  the 
properties  of  elements  and  compounds  permanently  modified 
under  certain  conditions?  In  attempting  to  find  a  solution, 
he  must  divide  the  phenomena  which  he  observes  into  their 
factors,  and  study  each  of  these  as  far  as  possible  indepen- 
dently of  the  others. 

The  chemist  need  not  regard  the  methods  pursued  by 
those  sciences  which  are  more  concrete  than  his  own, 
although  he  may  furnish  them  with  subject-matter  for  in- 
vestigation ;  inasmuch  however  as  the  science  of  matter  and 

1  The  abstract  and  the  general  truths  of  chemistry  are  scarcely  yet  so 
differentiated  as  to  allow  of  each  class  being  considered  separately.  I  do  not 
purpose  attempting  more  than  a  very  rough  separation  in  this  book. 


INTRODUCTORY.  5 

motion  is  a  more  abstract  science  than  that  of  chemistry,  he 
must  seek  help  for  his  work  in  the  methods  of  that  science, 
always  remembering  that  this  help  is  given  to  solve  chemical 
problems,  and  that  with  purely  physical  problems,  he,  as  a 
chemist,  is  not  concerned1. 

Pursuing  then  an  almost  purely  analytical  method  the 
chemist  finds  that  his  subject  branches  off  into  two  main 
divisions.  The  properties  of  bodies  are  modified;  he  studies 
the  relations  between  the  new  substances  and  those  by  the 
mutual  action  of  which  the  new  bodies  were  produced  :  but 
changes  in  the  properties  of  bodies  involve  a  consideration  of 
the  relative  positions  of  the  changing  body  and  of  other 
bodies,  in  other  words  involve  the  action  of  force  ;  he  en- 
deavours to  elucidate  the  laws  of  action  of  this  force. 

The  hypothesis  that  bodies  consist  of  small  parts — called 
molecules — in  motion,  is  one  of  the  lines  along  which  dyna- 
mical science  pursues  its  advance  into  the  sphere  of  chemistry. 
The  study  of  chemical  phenomena  is  also  brought  within  the 
pale  of  dynamical  methods  by  the  application  to  these  pheno- 
mena of  the  general  principles  of  the  conservation  and  de- 
gradation of  energy2.  The  latter  (thermo-dynamic)  method 
is  more  applicable  to  the  study  of  the  laws  of  chemical  forces 
than  of  the  properties  of  the  substances  depending  on  the 
actions  of  these  forces,  which  properties  have  been  chiefly 
elucidated  by  the  help  of  the  molecular  theory. 

We  may  indeed  study  relations  between  forces  accom- 
panying changes  in  the  distribution  of  certain  material  magni- 
tudes, which  we  may  call  molecules,  without  reference  to  what 
is  generally  known  as  the  molecular  theory  of  matter. 

But  it  seems  certain  that  no  chemical  phenomenon — and  it 
is  well  for  the  student  to  bear  in  mind  that  the  chemical  part 
is  always  but  one  aspect  of  any  natural  occurrence — can  be 
fully  explained  unless  both  methods  of  investigation  are 
applied  ;  unless  the  relations  between  the  reacting  bodies  and 
the  products  of  the  reaction,  and  the  relations  between  the 

1  Chemistry,  being  more  concrete,  is  less  exact  than  physics ;    mathematical 
'methods  can  scarcely  as  yet  be  applied  to  purely  chemical  data. 

2  See  Clerk  Maxwell :  Science  Conferences  at  South  Kensington,  1876. 


6  INTRODUCTORY. 

forces  exhibited  in  the  phenomenon  in  question,  are  con- 
sidered. 

In  the  following  pages  an  attempt  is  made  to  gather 
together  the  more  important  data  on  which  the  leading 
generalisations  of  chemistry  are  based,  and  in  the  light  of 
this  material  to  discuss  these  generalisations. 

By  the  use  of  the  terms  Chemical  Statics  and  Chemical 
Kinetics  I  would  indicate,  roughly,  that  the  phenomena  in- 
cluded under  the  first  of  these  headings  are  on  the  whole 
those  exhibited  by  chemical  bodies  or  systems  of  bodies  in 
equilibrium,  while  the  phenomena  classed  together  as  chemical 
kinetics  relate  more  to  bodies  or  systems  of  bodies  when 
chemically  active. 

It  may  seem  pedantic  to  make  use  of  terms  having  definite 
and  precise  significations  when  from  the  very  nature  of  the 
facts  they  can  be  employed  only  in  the  broadest  and  roughest 
way.  I  only  wish  to  indicate  that  the  subject-matter  of 
chemical  science  is  considered  in  this  book  as  divisible  into 
two  large  parts,  of  which  one  comprises  the  facts  and  prin- 
ciples concerned,  on  the  whole,  with  chemical  composition, 
and  the  other  those  which,  broadly  speaking,  relate  to  chemical 
action. 

It  will  of  course  be  found  that  chemical  occurrences  pre- 
sent, I  think  one  may  say  always  present,  both  statical  and 
kinetical  problems ;  the  two  sides  of  any  chemical  problem 
can  scarcely  be  regarded  apart,  in  the  present  state  of  know- 
ledge at  any  rate,  without  danger;  it  may  therefore  be  that 
phenomena  ranked  by  one  chemist  as  statical  would  by 
another  be  classed  as  kinetical. 

I  begin  by  considering  the  facts  and  principles  roughly 
classed  as  statical,  because  although  the  study  of  kinetics 
seems  naturally  to  precede  that  of  statics,  yet  in  chemistry 
our  knowledge  of  composition  is  much  in  advance  of  our 
knowledge  of  action  :  I  then  consider  the  data  and  generalisa- 
tions of  so-called  chemical  kinetics;  and  lastly  I  endeavour 
to  review  some  of  those  phenomena,  explanations  of  which, 
generally  only  very  partial  explanations,  can  be  gained,  or 
hoped  for,  only  by  the  help  of  both  methods. 


BOOK  I.  §  l] 


BOOK    I. 
CHEMICAL   STATICS. 

CHAPTER  I. 

ATOMS   AND   MOLECULES. 

1  THE  experimental  foundations  of  the  modern  chemical 
atomic  theory  were  laid  in  the  later  years  of  last  century 
by  the  German  chemist  Richter1.  The  work  of  Bergmann*, 
although  of  earlier  date  than  that  of  Richter,  cannot  be  re- 
garded of  equal  importance  as  concerns  the  history  of  the 
atomic  theory. 

Richter  studied  the  neutralisation  of  acids  by  bases,  and 
of  bases  by  acids,  and  shewed  that  a  definite  amount  of  acid 
(or  base)  always  combines  with  a  definite  amount  of  base 
(or  acid)  when  neutralisation  is  accomplished.  By  determining 
the  masses  of  various  bases  neutralised  by  one  and  the  same 
mass  of  each  acid,  and  the  masses  of  various  acids  neutralised 
by  one  and  the  same  mass  of  each  base,  Richter  was  able  to 
arrange  many  acids  and  bases  in  order  of  neutralisation. 
Fischer3,  in  1803,  published  the  first  table  of  chemical  equi- 
valents. Richter  had  given  a  series  of  numbers  for  each  base 
expressing  the  quantities  thereof  which  would  neutralise  1000 
parts  by  weight  of  sulphuric  acid,  or  1000  parts  of  hydro- 
chloric acid,  or  1000  parts  of  nitric  acid  &c. :  Fischer  saw 
that  it  was  sufficient  to  attach  a  single  number  to  each  base 
and  a  single  number  to  each  acid  ;  1000  parts  by  weight  of 

1  Ueber  die  nnuren  Gegenstande  der  Chemie,  1791 — 1802:  and  Anfangsgrundc 
der  Stochio metric  oiler  Messkunst  chemischer  Element 'f,  1822. 
-  Chemische  Werke,  2.  25  et  seq, 
3  In  a  note  to  Berthollet's  Essai  de  Statiqite  Chimiqtte  (1803). 


8  ATOMS  AND   MOLECULES.  [BOOK  I. 

sulphuric  acid  being  adopted  as  the  unit  of  neutralisation. 
Fischer's  numbers  expressed  the  masses  of  bases,  or  acids, 
which  were  of  equal  value  so  far  as  power  to  neutralise  a 
constant  mass  of  a  certain  acid  or  base  was  concerned1. 

Foreshadowings  of  the  atomic  theory  are  to  be  found  in 
a  work  by  W.  Higgins  entitled  A  comparative  view  of  the 
Phlogistic  and  Antiphlogistic  Theories,  -with  Inductions  (1791) 
[see  Henry's  Life  of  Dalton  p.  75  et  seql\\  but  to  Dalton  is 
undoubtedly  due  the  signal  honour  of  introducing  a  clear  and 
self-consistent  theory  regarding  the  composition  and  structure 
of  chemical  substances,  a  theory  which  in  its  essential  points 
has  stood  the  test  of  rigorous  experimental  verification,  and 
has  adapted  itself  to  the  wants  of  each  successive  school  of 
chemical  thought. 

2  Dalton2,  and  others,  found  that  elements  were  united  in 
many  compounds  in  fixed  proportions  by  weight,  and  more- 
over that  in  certain  compounds  of  one  element  with  others 
the  amount  by  weight  of  this  element  could  be  expressed  by 
whole  multiples  of  one  fundamental  number.  The  facts  re- 
garding the  quantitative  combinations  of  the  elements  are 
expressed  in  the  three  laws  of  chemical  combination  : — 

I.  The  masses  of  the  constituents  of  any  compound 

stand  in  an  unalterable  proportion  to  each  other 
and  to  the  mass  of  the  compound. 

II.  When  two  elements  combine  to  form  more  than  one 

compound  the  masses  of  one  of  the  elements 
which  combine  with  a  constant  mass  of  the  other 
element  bear  a  simple  relation  to  each  other. 

III.  The  masses  of  different  elements  which  severally 

combine  with  one  and  the  same  mass  of  another 
element  are  also  the  masses  of  those  different 

1  For  more  details  regarding  the  work  of  Richter  and  Fischer,  see  Wurtz,  The 
Atomic  Theory,  pp.  12 — 22. 

2  It  is  important  to  note  that  Dalton's  atomic  theory  was  conceived  by  him  in 
1802  from  considering  the  results  of  physical  experiments:  he  distinctly  states  in 
a  paper  on  the  absorption  of  gases  in  liquids  read  to  the  Manchester  Philosophical 
Society  in   that  year   that   he  had  lately  been    prosecuting    'with   remarkable 
success,'  'an  inquiry  into  the  relative  weights  of  the  ultimate  particles  of  bodies.' 


CHAP.  i.  §2]        DALTON'S  ATOMIC  WEIGHTS.  9 

elements  which  combine  with  each  other,  or  they 
bear  a  simple  relation  to  these  masses. 

To  account  for  the  facts'  of  chemical  combination  Dalton 
recalled  the  atomic  theory  of  the  Greek  philosophers ;  but  he 
transformed  an  interesting  speculation  about  the  possible 
causes  of  vaguely  observed  occurrences  into  a  scientific  theory 
of  quantitatively  established  facts. 

Every  chemical  substance,  simple  or  compound,  is  made 
up  of  atoms,  or  small  undivided  parts1 ;  the  properties  of 
each  substance  are  dependent  on  the  properties,  and  to  some 
extent  the  arrangement,  of  these  atoms:  the  old  hypothesis 
had  gone  as  far  as  this.  Dalton  added,  the  atom  of  every 
chemical  substance  has  a  definite  mass,  and  although  this 
mass  cannot  be  determined,  we  nevertheless  can  determine 
the  relative  masses  of  the  atoms  of  all  bodies.  It  is  only 
necessary  to  choose  some  substance  as  a  standard,  then  the 
mass  of  the  smallest  quantity  of  any  other  substance  which 
combines  with  the  unit  mass  of  the  standard  substance  repre- 
sents the  mass  of  the  atom  of  the  combining  substance  in 
terms  of  the  unit  chosen. 

As  this  point  is  of  supreme  importance  it  may  be  well 
that  we  should  have  Dalton's  own  words  before  us.  In  the 
New  System  of  Chemical  Philosophy  (1808)  after  discussing 
the  constitution  of  mixed  gases,  Dalton  proceeds  : 

"  When  any  body  exists  in  the  elastic  state  its  ultimate  particles  are 
separated  from  each  other  to  a  much  greater  distance  than  in  any  other 
state ;  each  particle  occupies  the  centre  of  a  comparatively  large  sphere, 
and  supports  its  dignity  by  keeping  all  the  rest,  which  by  their  gravity  or 
otherwise  are  disposed  to  encroach  upon  it,  at  a  respectful  distance. 
When  we  attempt  to  conceive  the  number  of  particles  in  an  atmosphere, 
it  is  somewhat  like  attempting  to  conceive  the  number  of  stars  in  the 
universe ;  we  are  confounded  by  the  thought.  But  if  we  limit  the  subject, 
by  taking  a  given  volume  of  any  gas,  we  seem  persuaded  that,  let  the 
divisions  be  ever  so  minute,  the  number  of  particles  must  be  finite;  just 
as  in  a  given  space  of  the  universe  the  number  of  stars  and  planets  cannot 
be  infinite. 

Chemical  analysis  and  synthesis  go  no  further  than  to  the  separation 

1  Dalton's  application  of  the  term  atom  to  the  small  chemically  indivisible 
parts  of  compounds,  seems  to  shew  that  he  did  not  regard  his  atoms  as  absolutely 
indivisible :  see  Life  by  Henry,  p.  88. 


IO  ATOMS  AND   MOLECULES.  [BOOK  I. 

of  particles  one  from  another,  and  to  their  reunion.  No  new  creation  or 
destruction  of  matter  is  within  the  reach  of  chemical  agency.  We  might 
as  well  attempt  to  introduce  a  new  planet  into  the  solar  system,  or  to 
annihilate  one  already  in  existence,  as  to  create  or  destroy  a  particle  of 
hydrogen.  All  the  changes  we  can  produce  consist  in  separating  particles 
that  are  in  a  state  of  cohesion  or  combination,  and  joining  those  that 
were  previously  at  a  distance. 

In  all  chemical  investigations  it  has  justly  been  considered  an  im- 
portant object  to  ascertain  the  relative  weights  of  the  simples  which 
constitute  a  compound.  But  unfortunately  the  inquiry  has  terminated 
here ;  whereas  from  the  relative  weights  in  the  mass,  the  relative  weights 
of  the  ultimate  particles  or  atoms  of  the  bodies  might  have  been  inferred, 
from  which  their  number  and  weight  in  various  other  compounds  would 
appear,  in  order  to  assist  and  to  guide  future  investigations,  and  to  correct 
their  results.  Now  it  is  one  great  object  of  this  work,  to  shew  the  im- 
portance and  advantage  of  ascertaining  the  relative  weights  of  the  ultimate 
particles  both  of  simple  and  compound  bodies,  the  number  of  simple 
elementary  particles  which  constitute  one  compound  particle,  and  the 
number  of  less  compound  particles  which  enter  into  the  formation  of  one 
more  compound  particle. 

If  there  are  two  bodies,  A  and  B,  which  are  disposed  to  combine,  the 
following  is  the  order  in  which  combination  may  take  place,  beginning 
with  the  most  simple  :  namely — 


I  atom   of  A  +  i  atom   of  B  = 

1  „        „  A +  2  atoms  „  B= 

2  atoms  „  A  +  i  atom    „  B= 
i  atom    „  A +3  atoms  „  B= 

3  atoms  „  A  +  i  atom    „  B= 


atom  of  C,  binary, 
„      „  D,  ternary, 
„       „  £,  ternary, 
„       „  f,  quaternary, 
„      „  G,  quaternary.'1 


&c.,  &c. 

Dalton  then  states  the  following  rules  respecting  chemical 
synthesis,  which  he  employed  in  determining  the  relative 
weights  of  the  smallest  chemically  indivisible  parts  of  com- 
pound bodies1. 

"  ist.  When  only  one  combination  of  two  bodies  can  be  obtained,  it 
must  be  presumed  to  be  a  binary  one,  unless  some  cause  appears  to  the 
contrary. 

2nd.  When  two  combinations  are  observed  they  must  be  presumed 
to  be  a  binary  and  a  ternary. 

•3rd.  When  three  combinations  are  obtained,  we  may  expect  one  to 
be  a  binary,  and  the  other  two  ternary. 

1  By  the  'smallest  chemically  indivisible  part'  of  a  substance  is  meant  an 
amount  such  that,  if  divided,  substances  (or  a  substance)  are  produced  different  in 
properties  from  the  original  substance. 


CHAP.  I.  §§  2,  3]    THE  DALTONIAN  THEORY.  1 1 

4th.  When  four  combinations  are  observed,  we  should  expect  one 
binary,  two  ternary,  and  one  quaternary."  &c.  &c. 

"  From  the  application  of  these  rules,"  Dalton  says,  "  to  the  chemical 
facts  already  well  ascertained,  we  deduce  the  following  conclusions : 
ist.  That  water  is  a  binary  compound  of  hydrogen  and  oxygen,  and 
the  relative  weights  of  the  two  elementary  atoms  are  as  i  :  7  nearly. 
2nd.  That  ammonia  is  a  binary  compound  of  hydrogen  and  azote,  and 
the  relative  weights  of  the  two  atoms  are  as  i  :  5  nearly.  ...In  all  these 
cases  the  weights  are  expressed  in  atoms  of  hydrogen  each  of  which  is 
denoted  by  unity." 

As  an  example  of  Dalton's  applications  of  these  rules, 
let  us  take  the  two  oxides  of  carbon.  These  two  oxides 
are  composed,  according  to  Dalton,  of  5-4  parts  by  weight  of 
carbon  combined  respectively  with  7  and  with  14  parts  by 
weight  of  oxygen :  the  first  of  these  bodies,  in  accordance 
with  Dalton's  second  rule,  was  considered  to  be  a  binary, 
and  the  second  a  ternary,  compound;  the  formulae  given  were 
CO  and  CO,  respectively.  [C  =  5-4,  O  =  7.] 

But  Dalton's  CO2  might  have  been  regarded  as  a  com- 
pound of  27  parts  by  weight  of  carbon  with  7  parts  by 
weight  of  oxygen,  in  which  case  its  formula  would  have 
been  written  CO  [C  =  27] ;  Dalton's  CO  would  then  have 
become  C2O  [C2  =  5'4J.  The  atomic  weight  of  carbon  would 
be  determined  as  2*7  or  5*4  according  as  carbon  monoxide 
or  carbon  dioxide  was  decided  to  be  a  binary  compound. 

At  a  later  time  it  was  said  by  some  chemists  that  a  binary 
compound  is  always  more  stable  than  a  ternary;  if  this  rule 
were  applied  to  the  case  of  the  oxides  of  carbon,  Dalton's 
number  for  the  atomic  weight  of  carbon  would  be  confirmed1. 
3  These  examples  illustrate  the  great  shortcoming  of  the 
Daltonian  theory:  the  atomic  weights  of  Dalton  are  either 
multiples  or  submultiples  of  a  certain  number,  but  we  can- 
not tell  what  multiple  or  what  submultiple.  Hydrogen 
being  taken  as  unity,  let  the  relative  masses  of  two  elements 
which  form  a  compound  B,  be  Q  and  Qlt  and  let  the  atomic 
weights  of  these  elements  be  A  and  A^  respectively;  then 
Q'.Q^'.-.nA  :  nvA^  where  «  and  n^  are  whole  numbers.  But 
inasmuch  as  the  values  of  n,  «,,  A,  and  Al  are  unknown,  it  is 

1  See  especially  Daubeny's  Atomic  Theory  (ind  edition  i8;o\  pp.  119 — 120. 


12  ATOMS   AND   MOLECULES.  [BOOK  I. 

evident  that  analysis  alone,  aided  by  the  Daltonian  theory, 
cannot  determine  the  atomic  weights  of  the  elements  which 
compose  the  substance  B. 

This  shortcoming  in  the  theory  could  not  be  supplied 
without  further  data:  Dalton  distinctly  states  that  in  order  to 
determine  the  number  of  elementary  atoms  in  the  atom  of  a 
compound  a  knowledge  of  the  composition  of  many  com- 
pounds of  the  given  elements  is  required. 

4  A  few  months  after  the  announcement  of  Dalton's   law 
of  multiple  proportions  and  atomic  theory,  Gay  Lussac  and 
Humboldt1  began  their  volumetric  investigations  which  cul- 
minated three  years  later  in  the  beautiful   discovery  of  the 
former  naturalist2,  that  gaseous   substances   unite    in   fixed 
volumetric  proportions  which  may  be  simply  expressed. 

There  is  a  constant  simple  relation,  said  Gay  Lussac, 
between  the  volume  of  a  gaseous  compound  and  the  volumes 
of  its  constituent  elements.  Let  one  volume  be  defined  as 
the  volume  occupied  by  unit  mass  of  hydrogen;  then  the 
combining  volume  of  any  gaseous  element  is  always  expressed 
by  a  whole  number;  e.g.  one  volume  of  nitrogen  combines 
with  one  volume  of  oxygen  to  form  two  volumes  of  nitric 
oxide,  two  volumes  of  hydrogen  and  one  volume  of  oxygen 
combine  to  form  two  volumes  of  water-gas,  one  volume  of 
nitrogen  and  three  volumes  of  hydrogen  form  two  volumes  of 
ammonia,  &c.  &c.  Condensation  sometimes  occurs,  some- 
times the  volume  of  the  compound  is  equal  to  the  sum  of  the 
volumes  of  the  combining  elements. 

This  discovery  appeared  to  add  fresh  arguments  to  the 
theory  of  Dalton.  The  ratios  of  the  masses  of  these  com- 
bining volumes  of  the  elements,  hydrogen  being  taken  as 
unity,  represent,  it  was  said,  the  relative  masses  of  the  atoms 
of  these  elements;  and  the  conclusion  was  drawn,  'equal 
volumes  of  gaseous  substances,  measured  at  the  same  tem- 
perature and  pressure,  contain  equal  numbers  of  atoms.' 

5  Dalton  however  refused  to  accept  Gay    Lussac's    gene- 
ralisation,  and  regarded  his  experimental    methods   as  un- 
trustworthy.    We    cannot,   I    think,    fail    to  be   struck  with 

1  Journal  de  Physique,  60.  129.  *  Mhu,  de  la  Soc.  d'Arciieil,  2.  207. 


CII.  I.  §§4-6]       AVOGADRO'S  ATOMS  AND  MOLECULES.  13 

the  justness  of  Dalton's  objection  to  the  statement  'equal 
volumes  contain  equal  numbers  of  atoms:'  he  argued  some- 
what as  follows : — one  volume  of  nitrogen  and  one  volume 
of  oxygen  form  two  volumes  of  nitric  oxide ;  but  one  atom 
of  nitrogen  and  one  atom  of  oxygen  form  one  atom  of  nitric 
oxide ;  therefore,  had  the  above  statement  been  correct,  the 
volume  of  nitric  oxide  would  have  been  equal  to,  not  twice 
as  great  as,  the  volume  of  oxygen  or  of  nitrogen.  So  again, 
one  atom  of  hydrogen  and  one  atom  of  oxygen  form  one 
atom  of  water,  according  to  Dalton's  rules  :  but  Gay  Lussac 
shewed  that  two  volumes  of  hydrogen  combine  with  one  volume 
of  oxygen  to  produce  two  volumes  of  water-gas  ;  hence  the 
atom  of  hydrogen  occupies  twice  the  volume  occupied  by  the 
atom  of  oxygen,  and  therefore  the  statement  of  Gay  Lussac 
is  incorrect.  If  Dalton's  definition  of  atom  and  his  rules 
regarding  atomic  synthesis  are  adopted,  Gay  Lussac's  state- 
ment that  '  equal  volumes  contain  equal  numbers  of  atoms ' 
must  be  abandoned. 

6  The  difficulty  was  removed  by  Avogadro1,  who  (in  1811) 
introduced  the  conception  of  two  kinds  of  small  particles : — • 
"molecules  int/grantes,"  or  as  we  should  now  say  molecules; 
and  "  molecules  e'le'mentaires"  or  as  we  should  now  say  atoms. 

The  molecules  of  elements  are  decomposed  in  chemical 
processes,  said  Avogadro,  and  the  atoms  unite  to  form  new 
compounds.  "Equal  volumes  of  gases  contain  equal  numbers 
of  molecules."  The  reaction  between  nitrogen  and  oxygen 
inexplicable  by  Gay  Lussac's  law  now  becomes  clear ;  each 
molecule  of  nitrogen  and  each  molecule  of  oxygen  divides 
into  two  parts,  and  these  parts  unite  to  form  the  new  mole- 
cules of  nitric  oxide ;  hence  there  are  twice  as  many  mole- 
cules of  nitric  oxide  produced  as  there  were  molecules  of 
nitrogen  or  oxygen  originally  present. 

By  thus  recognising  a  higher  order  of  atoms,  as  it  were, 
Avogadro  reconciled  Dalton's  theory  with  Gay  Lussac's 
results. 


1  Journal  de  Physique,  73.  58 :   also  Essai  d'tine  mantere  de  determiner  les 
lasses  relatives  des  molecules  element  air es  des  corps,  &c. 


14  ATOMS   AND    MOLECULES.  [BOOK  I. 

Ampere1  in  1814  drew  prominent  attention  to  the  hypo- 
thesis of  Avogadro,  and  attempted  by  its  help  to  explain  the 
structure  of  crystals.  But  the  hypothesis  had  come  before 
the  times  were  fully  ripe. 

7  Wollaston2  accepted  Dalton's  theory  but  proposed  to 
use  the  word  equivalent*  in  place  of  atom.  In  his  paper 
published  in  1814  (loc.  cit.)  Wollaston  drew  up  a  table  of 
equivalents  which  he  thought  would  be  serviceable  to  the 
practical  chemist  in  determining  the  amount  of  an  acid  which 
would  combine  with  a  given  weight  of  base,  or  the  weight  of 
precipitate  obtainable  in  a  given  reaction,  &c.  He  arranged 
his  numbers  on  a  scale  with  a  slider  attached,  and  adopted  a 
mechanical  contrivance  for  aiding  the  analyst  in  using  the  table. 
Although  Wollaston  employed  the  word  equivalent  in  place 
of  atom,  his  scale  and  table  must  be  regarded  as  helping  to 
extend  the  use  of  the  atomic  theory*.  For  the  practical  purpose 
which  he  had  in  view  Wollaston  did  not  deem  it  necessary  to 
adopt  any  theory;  at  the  same  time  he  regarded  the  atomic 
weights  of  Dalton,  especially  the  atomic  weights  of  compounds, 
as  too  hypothetical,  and  he  thought  that  equivalents  were  to 
be  preferred  for  most  purposes. 

Wollaston  referred  his  equivalent  numbers  to  oxygen  as 
10:  the  amount  by  weight  of  any  element  which  combined 
with  10  parts  by  weight  of  oxygen  was  regarded  by  him 
as  the  equivalent  of  that  element.  But  the  system  of 
equivalents  was  liable  to  the  same  objection  as  had  been 
urged  against  the  system  of  atomic  weights :  it  was  too 
vague. 

(1)  Thus  7'5  parts  by  weight  of  carbon    unite  with  20 
parts   by  weight   of  oxygen,  said  Wollaston,  therefore   the 
formula  of  the  compound  produced  is  CO2. 

(2)  Again  7*5  parts  by  weight  of  carbon  unite  with   10 
parts  by  weight  of  oxygen,  therefore  the  formula  of  the  com- 
pound produced  is  CO. 

1  Ann.  Chim.  Phys.  90.  43. 
-  Phil.  Trans,  for  1814,  r  et  seq. 

3  Wollaston  appears  to  have  first  used  this  term  in  1808  (Phil.  7'rans.). 

4  See  Cannizzaro,  C.  S.  Journal  [i],  10.  945. 


CHAP.  I.  §  7]  EQUIVALENTS.  15 

But  he  might  also  have  said 

(0  375  parts  by  weight  of  carbon  unite  with  10  parts 
by  weight  of  oxygen,  and  the  formula  of  the  product  is 
CO ;  and 

(2)  7-5  of  carbon  unite  with  10  of  oxygen,  therefore  the 
formula  of  the  compound  is  C2O. 

It  seemed  impossible  to  determine  the  equivalent  weight 
of  carbon,  just  as  in  Dalton's  system  it  was  impossible  to 
determine  the  atomic  weight  of  carbon1. 

If  the  unit  of  equivalency  is  8  parts  by  weight  of  oxygen, 
what  is  the  equivalent  of  copper  ?  An  electric  current  is 
passed  through  a  voltameter  and  also  through  molten  cuprous 
chloride ;  for  every  8  parts  by  weight  of  oxygen  set  free 
in  the  voltameter  63 '5  parts  by  weight  of  copper  appear  in 
the  second  vessel :  cupric  chloride  is  substituted  for  cuprous 
chloride,  and  now  3175  parts  of  copper  are  eliminated  for 
every  8  parts  of  oxygen.  So  in  the  compounds  of  copper 
and  oxygen,  we  have  in  one  case  63-5  of  copper  combined 
with  8  of  oxygen,  in  the  other  3175  of  copper  with  8  of 
oxygen. 

So  long  as  the  term  equivalent  was  applied  to  acids  and 
bases,  or  to  oxides,  it  had  a  definite  meaning.  The  mass  of 
oxide  which  neutralised  unit  mass  of  standard  acid  was  the 
equivalent  of  that  oxide,  because  it  was  equal,  so  far  as 
neutralising  power  went,  to  some  other  mass  of  another  oxide. 

"  When  we  speak  of  the  equivalent  of  a  body,"  said  Gerhardt,  "  we 
should  always  indicate  to  what  other  body,  to  what  functions,  to  what 
properties,  that  equivalent  corresponds."2 

Richter  shewed  that  there  is  a  constant  relation  between 
the  amount  of  oxygen  in  an  oxide  and  the  amount  in  the  acid 
which  neutralises  this  oxide :  e.g.,  in  sulphuric  acid,  he  said, 
the  oxygen  is  three  times,  and  in  nitric  acid  five  times,  that 
in  the  oxide  neutralised.  This  rule  was  made  general.  Now 

1  Thus  for  iron  we  have  the  equivalents  28  and  18*6:  for  carbon,  the 
equivalents  3,  4,  8,  and  12:  for  nitrogen,  4-6  and  2'^:  for  oxygen,  8  and  16 : 
for  silicon,  7  and  3-5,  &c.  £c.  Williamson,  C.  S.  Journal,  22.  328. 

1  Quoted  by  J.  J.  Griffin  in  The  Radical  Theory  in  Chemistry,  p.  32. 


1  6  ATOMS   AND   MOLECULES.  [BOOK  I. 

the  equivalent  of  aluminium1  was  said  to  be  1375:  the 
formula  of  sodium  sulphate,  in  accordance  with  Richter's  rule, 
was  written  NaO  .  SOg;  hence  the  formula  of  aluminium  sul- 
phate should  have  been  written  AUO  .  SO3  (1375x1  =  amount 
of  aluminium  uniting  with  8  parts  by  weight  of  oxygen)  ;  but 
the  formula  was  almost  invariably  written  A12O3  .  3SO3,  which 
is  a  departure  from  a  strictly  equivalent  notation. 

Mohr  (Meckanische  Theorie  der  Chemischen  Affinitaf),  who 
strongly  upheld  an  -equivalent  notation,  admits  (loc.  cit. 
pp.  143  —  144)  that  no  equivalency  exists  between  the  oxides 
RO  and  R2O3  ;  he  also  despairs  of  determining  the  equivalent 
of  phosphoric  acid.  Those  quantities  of  two  substances  are 
equivalent,  according  to  Mohr,  which  by  interaction  with 
other  bodies  produce  similar  compounds  ;  but  he  fails  to 
define  'similar  compounds,'  or  rather  he  admits  the  im- 
possibility of  finding  a  definition. 

That  the  masses  of  elements  which  mutually  combine 
do  not  always  represent  equivalent  quantities  of  these  ele- 
ments was  gradually  discovered  ;  but  the  so-called  equivalent 
notation  assumed  that  these  masses  do  represent  equivalent 
quantities  of  the  combining  elements. 

8  The  systems  of  chemical  notation  founded  respectively 
on  the  atomic  weights  of  Dalton  and  on  the  equivalents  of 
Wollaston  continued  to  hold  divided  sway  over  the  minds  of 
chemists2.  A  man  of  preeminent  powers  of  classification  was 
required. 

1  The  reasons  for  adopting  the  number  1375  were  somewhat  as  follows:  — 
28  parts  by  weight  of  iron  combine  with  8  of  oxygen,  therefore  the  equivalent  of 
iron  is  28;  but  in  ferric  chloride  28x2  parts  by  weight  of  iron  are  combined 
with  35-5  x  3  parts  by  weight  of  chlorine  (the  equivalent  of  chlorine  is  35-5,  be- 
cause this  is  the  mass  of  that  element  which  combines  with  unit  mass  of  hydrogen). 
Now  aluminium  chloride  is  very  similar  in  properties  to  ferric  chloride,  therefore, 
reasoning  from  analogy,  this  compound  contains  two  equivalents  of  aluminium  ; 
but  aluminium  chloride  is  composed  of  the  elements  aluminium  and  chlorine  com- 
bined in  the  ratio  27-5  :  (3  x  35-5),  therefore  tlie  equivalent  of  aluminium  is 


a  The  student  who  wishes  to  pursue  this  subject  -in  greater  detail  may  consult 
any  of  the  older  text-books,  on  the  laivs  of  combination  and  atomic  weights,  e.g. 
Turner's  Chemistry,  pp.  -212  —  235  ;  he  will  thus  become  persuaded  how  impossible 


(  HAP.  I.  §  8.]          BEKZELIUS'   ATOMIC   WEIGHTS.  "17 

The  system  of  chemical  classification  and  notation  elabo- 
rated by  Jacob  Berzelius  (1779 — 1848)  was  essentially  electri- 
cal. The  dualism  of  the  Berzelian  school  was  the  logical 
development  of  the  views  of  Lavoisier  concerning  salts,  and  of 
the  hypothesis  of  Davy  regarding  the  relations  between 
electrical  and  chemical  actions1.  At  present,  however,  this 
part  of  the  work  of  the  great  Swedish  chemist  does  not 
specially  concern  us. 

Berzelius  recognised  the  necessity  of  extending  the  general- 
isations already  made  concerning  the  combinations  of  atoms. 
To  say  that  when  two  elements  by  combining  together  form 
only  one  compound,  that  compound  is  composed  of  one 
atom  of  each  element,  was,  according  to  Berzelius,  not  fully 
warranted  by  facts. 

To  discover  the  laws  of  atomic  combinations  was  the  task 
that  Berzelius  proposed  to  himself.  He  argued  that  inasmuch 
as  the  number  of  compounds  formed  by  the  mutual  actions  of 
any  two  or  three  elements  is  evidently  very  limited,  there 
must  be  certain  laws  expressing  the  conditions  under  which 
alone  atoms  combine. 

Berzelius  regarded  Gay  Lussac's  law  of  gaseous  combi- 
nation— 'equal  volumes  contain  equal  numbers  of  atoms' — 
as  the  most  important  of  the  generalisations  made  concerning 
atomic  combinations,  but  he  restricted  the  application  of  this 
law  to  elementary  gases.  He  admitted  that  a  compound  gas 
might  be  composed  of  half,  or  even  less  than  half,  as  many 
atoms  as  composed  an  equal  volume  of  an  elementary  gas ; 
he  did  not  compare  the  atomic  composition  of  elementary 
and  compound  gases:  he  thus  evaded  the  objections  urged  by 
Dalton  against  the  law  of  Gay  Lussac,  and  at  the  same  time 
he  declined  to  accept  the  statement  of  Avogadro,  'equal 
volumes  contain  equal  numbers  of  molecules.' 

The  ratios  of  the  weights  of  the  combining  volumes  of 

it  was  to  determine  the  values  of  atomic  weights  with  certainty.  Some  interesting 
points  especially  regarding  the  proposal  to  give  two  equivalents,  or  atomic 
weights,  to  some  of  the  elements  will  be  found  in  Griffin's  Radical  Theory, 
PP-  30—43- 

1  For  a  brief  notice  of  the  system  of  Berzelius  regarding  the  constitution  of 
compounds  see  Chap.  n.  pp.  113—116. 

.M.  C.  2 


1 8  ATOMS   AND   MOLECULES.  [ROOK  I. 

elementary  gases  were  regarded  by  Berzelius  as  representing 
the  ratios  of  the  weights  of  the  atoms  of  those  elements  ; 
therefore  to  water,  nitric  oxide,  and  ammonia  he  gave  the 
formulae,  H2O,  NO,  and  NH3;  because  two  volumes  of  hydro- 
gen unite  with  one  volume  of  oxygen  to  form  water,  one 
volume  of  nitrogen  unites  with  one  volume  of  oxygen  to 
form  nitric  oxide,  and  ammonia  is  produced  by  the  union  of 
one  volume  of  nitrogen  with  three  volumes  of  hydrogen. 

But  the  volumetric  method  was  of  limited  application  to 
the  problems  of  chemical  synthesis.  Berzelius  attempted  to 
state  general  rules  with  regard  to  the  combinations  of  atoms. 
These  rules  referred  chiefly  to  the  compounds  of  oxygen, 
compounds  which  played  so  important  a  part  in  the  mineral 
chemistry  wherewith  Berzelius  largely  concerned  himself.  The 
most  important  of  the  Berzelian  rules  were  three. 

I.  If  an  element  forms  two  oxides  with  twice  as  much 

oxygen  by  weight  in  one  as  in  the  other,  that  with 
the  smaller  mass  of  oxygen  is  to  be  represented 
as  a  compound  of  one  atom  of  element  united  with 
one  atom  of  oxygen,  and  that  with  the  larger 
mass  of  oxygen  as  a  compound  of  one  atom  of 
element  with  two  atoms  of  oxygen. 

II.  If  an  element  forms  two  oxides,  one  of  which  con- 

tains one  and  a  half  times  as  much  oxygen  by 
weight  as  the  other,  that  with  the  less  oxygen  is 
to  be  represented  as  composed  of  one  atom  of 
element  and  one  atom  of  oxygen,  and  the  other 
compound  as  formed  by  the  union  of  two  atoms 
of  element  with  three  atoms  of  oxygen. 

III.  The  mass  of  oxygen  in  an  acid  is  a  simple  multiple 

of  the  mass  of  oxygen  in  any  base  with  which  the 
acid  combines1,  and  this  multiple  generally  also 
expresses  the  number  of  atoms  of  oxygen  in  the 
acid  :  thus  in  the  case  of  sulphuric  acid  and 
potash,  an  amount  of  acid  containing  24  parts 
by  weight  of  oxygen  neutralises  that  amount  of 

1  This  had  been  stated  by  Richter  many  years  before  Berzelius:  see  ante  p.  15. 


CHAP.  I.  §§8-9]         BERZELIUS'   ATOMIC   WEIGHTS.  19 

potash  which  contains  8  parts  by  weight  of  oxygen, 
therefore,  by  the  Berzelian  rule,  there  are  three 
atoms  of  oxygen  in  one  atom  of  sulphuric  acid. 
When  nitric  acid  neutralises  potash  there  are  40 
parts  by  weight  of  oxygen  in  the  acid  for  every  8 
parts  in  the  base  ;  therefore  an  atom  of  nitric  acid 
contains  five  atoms  of  oxygen. 

By  the  use  of  these  rules  Berzelius  determined  the  for- 
mulae of  many  metallic  oxides  and  salts.  While  he  was  thus 
engaged,  Dulong  and  Petit1  announced  their  '  law  of  atomic 
heats' ;  and  shortly  afterwards  Mitscherlich2  made  known  his 
'  law  of  isomorphism.' 

Berzelius  adopted  both  laws,  and  by  their  help3,  along 
with  his  own  rules,  he  drew  up  a  table  of  atomic  weights 
which  in  very  many  cases  were  almost  identical  with  those 
now  in  general  use. 

TABLE  OF  ATOMIC  WEIGHTS.    (Berzelius*.') 

Arsenic         75'33  Manganese  S7'°2  Silver         2i6-6i 

Calcium        41-03  Sodium  46-62  Silicon          44'47 

Chlorine        35'47  Phosphorus  31 '43  Nitrogen      14-18 

Iron               54'36  Mercury  202*86 

Iodine  123*2  Oxygen  i6'oo  Hydrogen  =  I. 

Carbon          12*25  Sulphur  32*24 

Berzelius  himself  admits  that  the  atomic  weights  deter- 
mined by  his  rules  are  in  many  cases  open  to  doubt  (Lehrbuch, 
1st  edition,  vol.  ill.  part  i.  pp.  87 — 102).  Berzelius  had  a 
remarkable  amount  of  tact ;  his  rules  were  empirical,  but  he 
balanced  probabilities  so  well  that  he  generally  got  the  best 
possible  result. 

9        The   separation   which  Berzelius    made  between  the  for- 
mulae of  elementary  and  compound  bodies,  and  his  refusal 

>  See  p.  49. 

8  See  pp.  69—76. 

s  Berzelius  formulated  the  law  of  isomorphism  in  its  bearing  on  the  problem  of 
determining  atomic  weights  thus  ;  (Lehrbuch,  3rd  ed.,  vol.  I.  p.  98)  when  one  body 
is  isomorphous  with  another  the  number  of  atoms  in  which  is  known,  then  the 
number  of  atoms  in  the  other  is  known  also,  because  isomorphism  is  a  mechanical 
consequence  of  identity  of  atomic  structure. 

4  Jahresberichte,  1828.  73. 

2 — 2 


-:20  ATOMS   AND   MOLECULES.  [BOOK  I 

to  accept  Avogadro's  hypothesis  while  admitting  Gay  Lussac's 
"generalisation,  led  him  to  a  very  curious  result. 

Two  volumes  of  hydrogen,  weighing  2,  combine  with  one 
volume  of  oxygen,  weighing  16,  to  form  two  volumes  of 
water-gas.  Therefore,  said  Berzelius,  two  atoms  of  hydrogen 
combine  with  one  atom  of  oxygen  to  form  one  atom  of  water- 
gas.  But  water  contains  less  oxygen,  relatively  to  hydrogen, 
than  any  other  known  oxide  of  hydrogen,  therefore  it  is 
better  to  regard  it  as  a  compound  of  one  atom  of  oxygen 
with  one  double  atom,  or  with  one  atom  itself  composed  of  two 
equivalents,  of  hydrogen.  Again,  in  the  formation  of  the 
lowest  oxide  of  nitrogen  two  volumes  of  nitrogen  combine 
with  one  of  oxygen ;  but  it  is  better  to  regard  the  nitrogen 
as  composed  of  double  atoms  each  occupying  twice  the 
volume  of  the  atom  of  oxygen.  Once  more;  hydrogen  and 
chlorine  combine  in  equal  volumes,  and  the  volume  of  the 
product — hydrochloric  acid  —  is  equal  to  the  sum  of  the 
volumes  of  its  constituents  ;  but  as  the  hydrogen  atom  was 
regarded  by  Berzelius  as  double,  he  wrote  the  atomic  syn- 
thesis of  hydrochloric  acid  as 

H2  +  C12  =  H2CI2. 
2  vols.  2  vols.     4  vols. 

These  results  are  evidently  to  be  traced  to  the  failure  of 
Berzelius  clearly  to  distinguish  atom  from  equivalent,  and  to 
his  refusal  fully  to  accept  the  distinction  between  atom  and 
molecule  enunciated  by  Avogadro1. 

To  the  great  French  chemists,  Dumas,  Gerhardt  and 
Laurent,  is  chiefly  due  the  introduction  into  general  use  of 
a  system  of  notation  and  classification  founded  on  Avogadro's 
distinction  between  atoms  and  molecules. 
10  Dumas  early  accepted  Avogadro's  hypothesis ;  from  the 
specific  gravities  of  gases  he  deduced  the  relative  weights  of 
the  molecules  of  these  gases :  in  order  to  gain  more  informa- 
tion regarding  molecular  weights  he  introduced  a  new  method 
for  finding  the  specific  gravities  of  gases.  By  this  method  he 

1  For  a  more  detailed  account  of  the  work  of  Berzelius  on  atomic  weights  see 
Ladenburg's  Entwickelnngsgeschiihtc  d?r  Chetnic,  pp.  89 — 100. 


CIIAI'.  I.  §10]   WORK  OF  GERHARDT  AND  LAURENT.      21 

determined  the  molecular  weight  of  sulphur  to  be  96,  and 
that  of  phosphorus  to  be  1 24 ;  but  from  the  analogy  of 
sulphur  compounds  with  those  of  oxygen,  from  various 
chemical  considerations  regarding  phosphorus  compounds, 
and,  I  think  we  must  add,  from  not  keeping  Avogadro's 
statement  quite  distinct  from  that  of  Gay  Lussac,  Dumas 
convinced  himself  that  these  results  were  incorrect.  The 
molecular  weight  of  mercury  also  seemed  to  be  abnormal. 
Dumas  knew  of  exceptions  to  the  law  of  Dulong  and  Petit. 
Mitscherlich's  law  of  isomorphism  remained  ;  but  Mitscherlich 
had  himself  shewn  that  the  same  compound  might  assume 
more  than  one  crystalline  form ;  how  then  could  trustworthy 
conclusions  regarding  atomic  structure  be  deduced  from  so 
vague  a  law  ?  Dumas,  and  indeed  chemists  generally,  began 
to  despair  of  the  whole  theory  of  atoms ;  they  tried  to  find 
relief  in  equivalents,  so  called,  and  in  spite  of  the  many 
difficulties  they  gradually  tended  towards  an  equivalent 
notation,  a  notation  which  nevertheless  they  could  not  make 
thoroughly  self-consistent,  but  which  seemed  to  involve  fewer 
hypotheses  than  that  founded  on  the  theory  of  atoms1. 

L.  Gmelin  even  regarded  the  law  of  fixity  of  composition 
as  only  true  under  special  conditions.  When  the  affinity 
between  two  bodies  is  small,  they  may  be  united,  said  Gmelin, 
in  almost  any  proportions,  when  the  affinity  is  large  they 
tend  to  combine  in  fixed  proportions.  A  number  may  be 
given  to  each  element  representing  the  relative  amount  of 
that  element  which  combines  with  other  elements  to  form 
stable  and  well-marked  compounds;  this  'combining  weight' 
may  be  called  '  atomic  weight,'  but  it  is  only  a  number. 
Gmelin  adopted  8  as  the  combining  weight  of  oxygen,  6  as 
that  of  carbon  &c.:  the  formula  of  water  on  his  system  again 
became  HO. 

The  notation  used  by  Gmelin  was  at  best  a  compromise, 
and  unsatisfactory,  but  it  was  very  generally  adopted  for  many 
years. 

Inorganic  chemistry  had  failed  to  introduce  an  accurate 

1  For  a  general  account  of  Dumas'  influence  on  chemical  theories  see  his 
Lt'.'0>is  stir  la  Philosophic  Chiiniqiie,  republished  in  1878. 


22  ATOMS   AND   MOLECULES.  [BOOK  I. 

and  satisfactory  theory  of  chemical  structure;  it  was  now  the 
turn  of  organic  chemistry  to  attempt  the  task. 
11  Among  the  most  ardent  followers  of  the  new  chemistry 
introduced  by  Dumas,  were  two  men  whose  names  are  ever  to 
be  associated  as  those  of  a  brilliant  pair  of  students  of  nature 
who  died  all  too  early  for  the  work  which  seemed  given  them 
to  do.  Gerhardt  and  Laurent  occupy  a  prominent  place 
among  the  modern  reformers  of  chemistry;  they  introduced 
order  into  chemical  notation,  and  system,  where  system  had 
been  conspicuous  by  its  absence1. 

In  criticising  the  system  of  so-called  equivalent  weights 
Gerhardt  adopted  the  only  true  method;  he  studied  actually 
occurring  chemical  reactions. 

In  a  number  of  reactions  between  compounds  of  carbon 
in  which  carbon  dioxide,  water,  and  ammonia  were  produced, 
Gerhardt2  found  that  when  so-called  equivalent  weights  of 
the  reacting  bodies  were  employed,  the  smallest  quantities  of 
these  three  compounds  produced  were  always  those  repre- 
sented by  the  formulae  C2O4,  H2O2,  and  NH3,  respectively 
(C  =  6,  N  =  14,  O  =  8).  He  therefore  concluded  that  these 
formulae,  rather  than  the  commonly  accepted  formulae,  CO2, 
HO  (and  NH8),  must  represent  equivalent  weights  of  the 
compounds  in  question.  Similarly  he  concluded  that  the 
equivalent  formulae  of  sulphur  dioxide  and  carbon  monoxide 
must  be  S2O4  and  C2O2  respectively  (S=i6,  O  =  8,  C  =  6): 
and  arguing  from  these  conclusions  he  thought  himself 
justified  in  saying  that  the  true  equivalents  of  carbon,  sulphur, 
and  oxygen,  are  12,  32,  and  16,  and  not  6,  16,  and  8,  as 
generally  adopted.  Gerhardt  likewise  applied  his  acute 
reasoning  powers  to  an  examination  of  the  arguments  which 
determined  Berzelius  and  others  to  adopt  formulae  represent- 
ing weights  of  four  volumes  of  many  carbon  compounds ; 
these  arguments  he  proved  to  be  fallacious. 

Laurent  examined  the  groundwork  on  which  the  systems 

1  Laurent's  Chemical  Method  (Cavendish  Society  Publications)  gives  a  general 
account  of  the  more  important  work  of  these  chemists. 

2  J-  fur  prakt.  Chemie,  27.  439;  and  Ann.  Chim.  Phys.  [3]  7.  129:  and  8. 


CHAP.  i.  §  1 1]         LAURENT'S  NOTATION.  23 

of  equivalent  and  atomic  notation  were  based.  His  methods 
of  reasoning  were  founded  on  experimentally  determined 
facts,  hence  their  irresistible  force.  If  formulae  are  to  re- 
present equivalent  masses  of  substances,  then  said  Laurent, 
a  standard  must  be  adopted.  But  it  had  been  frequently 
shewn  that  the  quantities  represented  by  so-called  combin- 
ing weights  were  not  always  mutually  equivalent.  Power  of 
neutralising  unit  mass  of  standard  substance  might  be  adopted 
as  the  reaction  on  which  to  base  the  system,  but  this  method 
could  be  applied  only  to  a  limited  number  of  substances. 

The  idea  of  equivalency  is  associated  with  function.  What 
is  a  given  substance  capable  of  doing?:  this  question  must 
be  answered  before  the  equivalent  of  the  substance  can  be 
determined.  But  in  one  action  certain  weights  of  two  bodies 
may  be  equivalent,  while  altogether  different  weights  of  the 
same  bodies  are  equivalent  in  another  reaction. 

Laurent  affirmed  that  it  was  possible  to  found  a  systematic 
notation  on  equivalent  weights  assigned  to  the  elements. 
Thus,  in  ferrous  oxide  28  parts  by  weight  of  iron  are  combined 
with  8  parts  by  weight  of  oxygen;  let  Fe  =  28,  then  ferrous 
sulphate  is  represented  by  the  formula  Fe2SO4:  but  in  ferric 
oxide  there  are  2.^  (i.e.  i8'6)  parts  by  weight  of  iron  for 
every  8  parts  by  weight  of  oxygen ;  let  fe  =  1 8'6,  then  the 
formula  for  ferric  sulphate  is  fe2SO4.  The  formulae  Fe2SO4 
and  fe2SO4  represent  strictly  equivalent  quantities  of  the  two 
sulphates  of  iron.  So  also  if  the  composition  of  potassium- 
hydrogen  sulphate  is  expressed  by  the  formula  KHSO4,  then, 
in  a  system  of  notation  founded  on  equivalent  weights,  the 
composition  of  the  double  sulphate  of  potassium  and  alu- 
minium is  represented  by  the  formula  K^A1|SO4  (Al  =  27'3). 
But  such  a  notation  is  inconvenient,  and  it  frequently  conceals 
most  important  facts:  e.g.  in  a  strictly  equivalent  notation 
the  differences  between  monobasic  and  polybasic  acids  dis- 
appear ;  thus,  the  compositions  of  the  masses  of  monobasic 
hydrochloric  acid,  dibasic  sulphuric  acid,  and  tribasic  phos- 
phoric acid,  which  severally  neutralise  equal  masses  of  potash, 
are  expressed  by  the  formulae  HC1,  HS^O,,  and  HP^^.  re- 
spectively (Cl  =  35-5,  S  =  32,  O  =  16,  P  =  31). 


24.  ATOMS   AND   MOLECULES.  [BOOK  I. 

Laurent  returned  to  the  generalisation  of  Avogadro  and 
made  that  the  basis  of  his  system;  he  clearly  distinguished 
between  molecules  and  atoms,  and  he  applied  the  law  of  equal 
volumes  and  equal  numbers  to  molecules  only.  He  admitted 
that  apparent  exceptions  to  the  Avogadrean  law  existed, 
e.g.  the  molecules  of  sulphuric  acid  and  salammoniac  vapour 
appeared  to  occupy  twice  the  volume  occupied  by  the  mole- 
cule of  hydrogen;  but  he  said  that  this  hypothesis  gene- 
ralised the  facts  better  than  any  other  which  had  been  pro- 
posed. 

Laurent  founded  his  system  on  an  atomic  basis,  and  a 
fundamental  point  was  the  distinction  between  atom  and 
molecule.  He  adopted  formulae  representing  two  volumes: 
the  facts  of  'nascent'  action  he  sought  to  explain  by  the  con- 
ception of  atoms  as  distinct  from  molecules.  A  molecule  he 
defined  to  be  "the  amount  of  a  gaseous  substance  which 
occupies  twice  the  volume  occupied  by  an  atom  of  hydro- 
gen," or,  "the  smallest  amount  of  a  substance  capable  of 
taking  part  in  a  chemical  reaction."  An  atom  he  defined  as 
"the  smallest  amount  of  an  element  which  enters  into  the 
composition  of  a  compound."  Here  we  have  the  application 
of  the  term  molecule  to  elements  and  compounds  alike,  while 
atom  is  used  of  elements  only. 

Equivalents  are  the  amounts  of  bodies  which  are  of  equal 
value  in  performing  a  stated  action. 

Gerhardt  and  Laurent  adopted  the  laws  of  atomic  heat 
and  isomorphism  as  aids  in  determinations  of  atomic  weights. 
12  Chemical  evidence  in  favour  of  the  division  of  elementary 
molecules  during  chemical  changes  was  accumulated  by 
Brodie,  Wurtz,  Williamson  and  others;  but  the  work  of  these 
chemists  will  be  referred  to  in  more  detail  when  we  come  to 
speak  of  the  chemical  methods  for  determining  molecular 
weights  (see  pp.  79—85). 

Thus,  at  last,  we  have  arrived  at  a  clear  separation  between 
the  meanings  of  the  terms  atom,  molecule,  equivalent. 

The  system  now  adopted  in  chemistry  is  essentially  that 
of  Gerhardt  and  Laurent;  it  is  founded  on  the  conception  of 
atoms  and  molecules.  Dalton's  fundamental  idea  has  been 


CHAP.  I.  §§  12-13]      MOLECULAR   THEORY   OF    MATTER.          2$ 

amply  confirmed  by  modern  research.  We  have  maintained 
the  idea  of  equivalency,  but  we  no  longer  speak,  as  Wollaston 
did,  of  the  equivalent  of  an  element ;  we  compare  the 
elementary  atoms  among  themselves  and  arrange  them  in 
groups,  all  the  members  of  each  of  which  are  equivalent  in 
respect  of  a  certain  definite  action  they  are  capable  of  per- 
forming. 

A  true  and  fundamental  conception  once  gained  in  science 
is  never  lost;  it  may  be  largely  modified,  it  may  even  appear 
at  times  to  be  abandoned,  but  it  develops  slowly  and  bears 
much  fruit  at  last. 

The  vicissitudes  in  the  fortunes  of  a  truly  scientific  idea  are 
aptly  illustrated  by  the  history  of  the  atomic  theory.  After  a 
period  of  dormancy  of  more  than  2000  years,  the  atomic 
theory  was  revived  and  rendered  definite  by  Dalton;  was 
firmly  established  on  an  experimental  basis  by  Berzelius;  was 
almost  abandoned  by  the  school  founded  by  the  same 
chemist;  was  rehabilitated  and  again  nearly  despaired  of  by 
Dumas;  was  largely  advanced  by  Avogadro;  was  subdivided 
and  its  parts  clearly  distinguished  by  Gerhardt  and  Laurent, 
and  is  now  the  foundation-stone  of  a  great  and  ever-increasing 
edifice. 

13  Thus  far  I  have  dealt  with  the  development  of  the  atomic 
and  molecular  theory  regarded  almost  entirely  from  the 
chemical  point  of  view.  So  great  however  is  the  importance 
of  clearly  perceiving  the  position  which  this  theory  occupies 
in  modern  chemistry,  and  of  realising  the  nature  of  the 
physical  evidence  on  which,  in  its  more  recent  development, 
the  theory  so  largely  rests,  that  I  must  endeavour  very  briefly 
to  give  a  sketch  of  that  evidence,  remembering  always  that 
it  is  as  chemists,  not  as  physicists,  that  we  are  interested  in 
this  subject. 

There  are  two  general  theories  of  the  structure  of  material 
substances:  one  assumes  that  apparently  homogeneous  bodies 
are  really  homogeneous  throughout ;  a  theory  which  is  in- 
capable of  explaining  the  observed  properties  of  matter ; 
and  the  other  asserts  that  apparently  homogeneous  bodies 
are  possessed  of  a  grained  structure. 


26  ATOMS   AND   MOLECULES.  [BOOK  I. 

Viewed  from  a  distance,  a  brick  wall,  or  a  body  of  soldiers, 
appears  to  be  one  reddish-coloured  homogeneous  mass,  but  a 
nearer  observer  sees  that  the  wall  is  made  up  of  distinct  parts, 
that  the  company  is  composed  of  individual  men. 

The  molecular  theory  supposes  that  were  our  senses 
sufficiently  acute,  we  should  see  the  grains  or  particles  of 
which  an  apparently  homogeneous  mass  of  matter  is  com- 
posed. 

The  theory  begins  by  assuming  that  any  material  body 
"is  made  up  of  parts  (each  of  which  is  capable  of  motion), 
and  that  these  parts  act  on  each  other  in  a  manner  consistent 
with  the  principle  of  the  conservation  of  energy."1  These 
parts  are  called  molecules. 

The  dynamical  conception  of  a  gaseous  molecule  is  "  That 
minute  portion  of  a  substance  which  moves  about  as  a  whole,  so 
that  its  parts,  if  it  has  any,  do  not  part  company  during  the 
motion  of  agitation  of  the  gas?* 

This  conception  is  entirely  independent  of  chemical  facts. 

All  the  molecules  of  one  element  are  of  the  same  mass, 
else  differences  would  be  observed  in  the  properties  of  different 
parts  of  an  elementary  gas,  e.g.  hydrogen ;'  such  differences 
arising  from  the  separation  of  the  gas  into  portions  each  more 
or  less  unlike  the  others. 

The  relations  between  the  motions  and  the  space  occupied 
by  these  little  parts,  assuming  their  existence  and  mutual 
independence,  may  be  dynamically  deduced  by  the  aid  of  a 
theorem  of  Clausius,  and,  with  a  justifiable  assumption  as  to  the 
dynamical  meaning  of  temperature,  the  equation  thus  arrived 
at  expresses  with  considerable  accuracy  the  relations  actually 
existing  between  temperature  and  pressure,  and  volume,  in  the 
case  of  rarefied  gases ;  the  equation,  that  is  to  say,  expresses 
the  laws  of  Charles  and  Boyle.  When  the  gas  is  more 
condensed  the  equation  ceases  to  express  the  relations 
existing  between  temperature  and  pressure,  and  volume : 
hence  the  theory  asserts  the  existence  in  such  a  gas  of  mutual 
attractions  or  repulsions  between  the  little  parts,  or  mole- 

1  Clerk  Maxwell,  Article  'Atom'  In  Encycl,  firilannica.     (Qth  Ed.) 
»  IbiJ. 


CHAP.  I.  §  13]     MOLECULAR  THEORY  OF  MATTER.      2/ 

cules ;  it  asserts  that  these  parts  are  no  longer  mutually 
independent. 

"The  hypothesis  that  a  gas  consists  of  molecules  in  motion,  which 
act  on  each  other  only  when  they  come  together  during  an  encounter, 
but  which  during  the  intervals  between  their  encounters — which  con- 
stitute the  greater  part  of  their  existence — are  describing  free  paths,  and 
;ire  not  acted  on  by  any  molecular  forces,"1 

having  been  justified  by  dynamical  reasoning,  the  next  step 
is  made  by  investigating  mathematically  the  properties  of 
such  a  system  of  molecules.  And  one  deduction  thus  made 
is  "  If  equal  volumes  of  two  gases  are  at  equal  temperatures  and 
pressures,  tlie  number  of  molecules  in  each  is  the  same,  and 
therefore  the  masses  of  the  two  kinds  of  molecules  are  in  the 
same  ratio  as  the  densities  of  the  gases  to  wJiich  they  belong."* 

This  statement  is  of  paramount  importance  to  the  chemist, 
inasmuch  as  on  it  is  based  his  system  of  molecular  weights. 
It  is  very  necessary  to  bear  in  mind  that  this  proposition  is 
deduced  by  dynamical  reasoning  from  a  simple  hypothesis  as 
to  the  structure  of  matter,  itself  justified  by  many  facts. 

By  analogous  reasoning,  various  deductions  are  made 
from  the  theory,  which  express  generalisations  of  experi- 
mentally determined  facts  concerning  gaseous  phenomena3. 

Passing  to  more  complex  occurrences,  the  molecular  theory 
gives  a  simple  explanation  of  the  diffusion  of  matter,  diffusion 
of  motion,  and  diffusion  of  heat  in  gases  ;  these  phenomena 
being  regarded  by  the  theory  as  dependent  on  the  frequency 
of  the  molecular  encounters,  and  on  the  nature  of  the  actions 
between  the  encountering  molecules. 

The  molecular  theory  has  also  been  successfully  applied 
to  explain,  broadly,  many  of  the  phenomena  of  evaporation, 
condensation,  electrolysis,  and  spectroscopy. 

To  explain  spectroscopic  phenomena  it  is  apparently 
necessary  to  assume  molecules  to  be  elastic  substances,  but 
elasticity  is  just  the  property  of  matter  to  explain  which  the 

1  Clerk  Maxwell,  Article  'Atom'  in  Encycl.  Brit. 

-  Ibid.  Strictly  speaking  this  statement  applies  only  to  perfett  gases,  i.e.  gases 
the  molecules  of  which  are  without  action  on  each  other. 

3  For  some  of  the  most  important  of  these  see  Clerk  Maxwell's  Theory  of 
Heat,  pp.  307 — 322  (6th  edition). 


28  ATOMS   AND   MOLECULES.  [BOOK  I. 

molecular  hypothesis  was  first  assumed.  The  theory  of 
'  vortex  atoms/  developed  by  Sir  William  Thomson  from  the 
original  conception  of  Helmholtz,  explains  spectroscopic 
facts — and  generally  those  facts  which  must  be  explained  by 
a  successful  molecular  theory — better  than  any  other  which 
has  yet  been  suggested.  A  short  account  of  this  theory  will 
be  found  in  the  article  'Atom'  in  the  last  edition  of  the 
Encyclopedia  Britannica,  where  we  read 

"  The  success  of  this  theory  in  explaining  phenomena  does  not  depend 
on  the  ingenuity  with  which  its  contrivers  'save  appearances'  by  intro- 
ducing first  one  hypothetical  force  and  then  another.  When  the  vortex 
atom  is  once  set  in  motion  all  its  properties  are  absolutely  fixed,  and 
determined  by  the  laws  of  motion  of  the  primitive  fluid  which  are  fully 
expressed  in  the  fundamental  equation."1 

Attempts  have  been  made  to  determine  the  absolute  size 
of  molecules2,  and  although  the  results  must  be  regarded  as 
but  rough  estimates,  nevertheless  they  shew  that  to  measure 
molecules  is  a  legitimate  object  of  scientific  investigation. 
The  smallest  portion  of  matter  visible  by  the  help  of  a  good 
microscope  may  be  taken  to  be  a  cube  each  side  of  which 
measures  4^-^th  of  a  millimetre  in  length ;  such  a  cube  will 
contain,  according  to  the  rough  measurements  hitherto 
made,  from  60  to  100  millions  of  molecules3. 

The  foundations  of  a  truly  mathematical  theory  of  the 
structure  of  matter  have  been  laid  by  Helmholtz  and  Thom- 
son in  their  theory  of  vortex  atoms ;  but,  apart  from  this,  the 
fact  that  the  proposition  commonly  known  as  Avogadro's 
law  may  be  deduced  by  dynamical  reasoning  from  a  simple 
hypothesis  which  admits,  although  as  yet  only  to  a  limited 
extent,  of  the  application  of  mathematical  methods,  and 
which  is  justified  by  a  large  number  of  physical  facts,  suffices 
to  make  that  law  of  extreme  importance. 

Attempts  have  recently  been  made  to  apply  to  certain- 
chemical  phenomena  a  more  strictly  dynamical  method  of 

1  For  a  few  more  details  regarding  the  application  of  this  theory  to  chemical 
occurrences  see  Book  II.  Chap.  in. 

2  See  especially  Sir  W.  Thomson,  Nature  1.  p.  551,  and  also  28.  pp.  203, 
1  so,  274. 

3  Clerk  Maxwell,  Ice.  cit. 


CUAP.I.  §§  13-14]         PARTS   OF    MOLECULES.  29 

reasoning  than  is  employed  in  the  molecular  theory,  the 
methods  of  which  are  essentially  statistical ;  these  will  be 
referred  to  under  the  second  main  division  of  this  book. 

An  atomic  theory  has  been  elaborated  by  the  chemist ;  a 
molecular  theory  of  matter  has  been  propounded  by  the 
physicist,  and  has  been  advanced  so  far  as  to  allow  of  wide 
conclusions  being  deduced  therefrom  by  dynamical  reasoning  ; 
no  theory  asserting  the  continuity  of  matter  has  been  found 
capable  of  explaining  the  observed  phenomena  of  matter ; 
hence  to  accept  the  molecular  theory,  as,  at  present,  the  only 
feasible  working  hypothesis,  is  simply  to  obey  the  dictates  of 
the  scientific  method. 

14  Let  us  then  turn  to  the  applications  of  this  theory  to  che- 
mical facts.  It  is  well  to  repeat  the  terms  in  which  Clerk 
Maxwell  has  expressed  the  physical  conception  of  the  mole- 
cule : — "  A  gaseous  molecule  is  that  minute  portion  of  a  sub- 
stance which  moves  about  as  a  w]iole,  so  that  its  parts,  if  it  has 
any,  do  not  part  company  during  the  motion  of  agitation  of  the 
gas."  One  of  the  deductions  from  this  conception  is  that 
equal  volumes,  of  so-called  perfect  gases,  measured  at  the  same 
temperature  and  pressure,  contain  equal  numbers  of  molecules. 

This  statement  must  now  be  applied  to  chemical  interac- 
tions between  gases. 

Consider,  for  instance,  the  combination  of  hydrogen  with 
chlorine  and  that  of  nitrogen  with  hydrogen. 

Hydrogen  combines  with  chlorine  to  form  hydrochloric  acid. 
2  vols.        combine  with    2  vols.        „         4  vols.        „ 

But  since  equal  volumes  of  gases  contain  equal  numbers 
of  molecules,  and  since  each  molecule  of  hydrochloric  acid  is 
composed  of  both  hydrogen  and  chlorine,  it  is  evident  that 
each  molecule  of  hydrogen  by  combination  with  one  molecule 
of  chlorine  produces  not  one  but  two  molecules  of  hydrochloric 
acid. 

So  again, 

Nitrogen  combines  with  hydrogen  to  form  ammonia. 
2  vols.       combine  with   6  vols.  „         4  vols. 

Here  again  each  nitrogen  molecule  has  given  rise  to  two 


30  ATOMS   AND   MOLECULES.  [BOOK  I. 

molecules  of  ammonia.  Hence  it  is  evident  that  although  the 
parts  of  a  molecule  of  hydrogen,  nitrogen,  or  chlorine  "  do  not 
part  company  during  the  motion  of  agitation  of  the  gas  "  to 
which  the  molecule  belongs,  these  parts  nevertheless  do  part 
company  in  those  chemical  reactions  which  are  stated  above. 
When  various  reactions  between  gaseous  substances  are 
studied  this  conclusion  is  found  to  hold  good  throughout 
a  large  range  of  chemical  phenomena.  Hence  the  chemist 
is  obliged  to  recognise  a  portion  of  matter  smaller  than 
the  molecule ;  this  smaller  portion  of  matter,  this  part  of 
a  molecule,  is  the  atom1. 

In  the  above  and  in  other  reactions  it  is  shewn  that  the 
molecules  of  hydrogen,  nitrogen,  and  chlorine  split  into  at  least 
two  parts  when  these  molecules  act  chemically  on  each  other 
or  on  other  molecules ;  hence,  if  the  symbols  H,  Cl,  and  N,  are 
used  to  denote  an  atom  of  hydrogen,  chlorine,  and  nitrogen, 
respectively,  the  molecules  of  these  three  elements  may  be 
represented  by  the  symbols  H2,  C12,  and  N2.  These  symbols 
represent  the  masses  of  equal  volumes  of  the  three  elements ;  if 
one  of  these  masses  be  taken  as  the  unit,  the  others  are 
evidently  the  masses  of  the  molecules  of  the  gases  in  question 
referred  to  this  unit ;  because  equal  volumes  contain  equal 
numbers  of  molecules,  and  therefore  '  the  masses  of  the  two 
kinds  of  molecules  are  in  the  same  ratio  as  the  densities  of  the 
gases  to  which  they  belong.' 

Hydrogen  is  the  universally  adopted  standard  of  reference 
for  molecular  and  atomic  weights :  the  atomic  weight  of 
hydrogen  is  taken  as  unity,  and  therefore,  according  to  the 
reasoning  sketched  above,  the  molecular  weight  of  this  element 
is  not  less  than  two. 

But  it  might  be  urged  that  when  molecules  of  hydrogen 
and  chlorine  interact,  each  molecule  separates  into  more  than 
two  parts,  into  3,  4,  5,  &c.  parts.  Granting  '  Avogadro's  law,' 
the  data  given  on  p.  29  shew  that  the  number  of  molecules  of 

1  It  is  well  to  note  that  the  molecular  theory  of  matter  as  applied  to  chemical 
phenomena  does  not  assert  or  deny  the  finite  divisibility  of  matter.  In  C.  S. 
Journal  [2],  13.  501,  there  is  a  most  interesting  paper  by  Clerk  Maxwell  on  '  The 
dynamical  evidence  of  the  molecular  constitution  of  bodies.' 


CHAP.  I.  §  14]  PARTS   OF    MOLECULES.  31 

hydrochloric  acid  produced  is  twice  the  number  of  molecules 
of  hydrogen  or  chlorine  which  have  interacted  to  produce 
them ;  therefore,  if  each  molecule  of  hydrogen  and  each  of 
chlorine  has  separated  into,  say,  four  parts,  each  molecule  of 
hydrochloric  acid  must  be  composed  of  two  of  those  parts  of 
hydrogen  and  two  of  chlorine.  But  if  this  is  so,  it  ought  to 
be  possible  to  remove  the  hydrogen,  or  the  chlorine,  from  a 
molecule  of  hydrochloric  acid  in  two  separate  portions ;  in 
other  words,  interactions  ought  to  occur  between  hydrochloric 
acid  and  other  bodies,  not  themselves  compounds  of  hydrogen 
or  chlorine,  resulting  in  the  evolution  of  hydrogen,  or  chlorine, 
and  the  production  of  a  new  compound,  or  new  compounds,  of 
chlorine,  hydrogen,  and  the  interacting  body  or  constituents 
of  this  body.  But  no  such  interactions  occur ;  therefore  hydro- 
gen, or  chlorine,  cannot  be  removed  in  parts  from  a  molecule 
of  hydrochloric  acid  ;  if  the  molecule  is  decomposed  and 
hydrogen,  or  chlorine,  is  removed,  the  whole  of  the  hydrogen, 
or  chlorine,  is  removed.  Therefore  it  is  extremely  improbable 
that  a  molecule  of  hydrochloric  acid  is  built  up  of  more  than 
one  small  chemically  indivisible  part,  or  atom,  of  each  of  the 
elements  which  compose  it ;  and  therefore  it  is  extremely  im- 
probable that  when  molecules  of  hydrogen  and  chlorine 
interact  to  produce  molecules  of  hydrochloric  acid,  each  mole- 
cule of  hydrogen,  or  chlorine,  separates  into  more  than  two 
parts  or  atoms.  Therefore,  as  we  have  agreed  to  regard  the 
weight  of  an  atom  of  hydrogen  as  unity,  we  say  that  the 
molecular  weight  of  hydrogen  is  two. 

The  modern  molecular  theory  of  matter  is  not  identical 
with  the  atomic  theory  of  Dalton  ;  it  is  based  on  evidence  of 
a  different  kind  ;  it  is  essentially  a  physical  and  dynamical 
theory,  although  strengthened  by  chemical  arguments.  The 
atomic  theory  of  modern  chemistry  may  be  regarded  as  grow- 
ing out  of  the  application  of  reasoning  founded  on  chemical 
facts  to  the  molecular  theory  of  matter. 

Assuming  'Avogadro's  law,'  and  remembering  that  the 
molecule  of  hydrogen,  which  is  the  standard  body  in  terms  of 
which  all  other  molecular  weights  are  stated,  divides  into  at 
least  two,  and  probably  into  only  two,  parts  in  many  chemical 


32  ATOMS   AND   MOLECULES.  [BOOK  I. 

changes,  we  arrive  at  the  practical  definition  of  molecular 
weight. 

The  molecular  weight  of  a  gas  is  the  weight  of  that  volume 
thereof  which  is  equal  to  the  volume  occupied  at  the  same  tem- 
perature and  pressure  by  two  parts  by  weight  of  hydrogen^. 

In  determining  the  specific  gravity  of  a  gas  it  is  easier, 
and  less  liable  to  error,  to  find  the  weight  of  the  vessel  filled 
with  air  than  with  hydrogen  ;  the  result  is  therefore  stated  as 
specific  gravity  referred  to  air  as  unity.  Now  the  specific 
gravity  of  hydrogen  is  -06926  [air=  i];  the  molecular  weight 
required  is  equal  to  twice  the  specific  gravity  of  the  gas 
referred  to  hydrogen ;  hence  if  M=  molecular  weight,  and 

d—  specific  gravity  referred  to  air  as  unity, M=—^ — ^=28*87  d. 

Hence  the  practical  rule  for  determining  the  molecular  weight 
of  a  gas  : — 

Find  tJie  specific  gravity,  i.e.  the  ratio  between  the  weights 
of  equal  volumes  of  the  gas  and  air  under  the  same  conditions 
of  temperature  and  pressure,  and  multiply  this  by  28-87. 
15        The  following  table  presents  the  results  hitherto  obtained 
regarding  the  molecular  weights  of  elementary  gases. 

1  The  volume  occupied  by  two  parts  by  weight  of  hydrogen,  or  twice  the 
volume  occupied  by  unit  mass  of  hydrogen,  is  often  called  two  volumes. 


CHAP.  I.  §  15]    MOLECULAR  WEIGHTS  OF  ELEMENTS. 


33 


[The  numbers  in  column  v  are  not  always  exactly  equal  to  the  products 

obtained  in  column  IV ;  for  an  explanation  see  par.  17.] 

Molecular  weights  of  elementary  Gases. 


I 

Name  of  element 

II 

Spec,  gravity 
(air=i) 

III 

Temp,  of 
observation 

IV 

Sp.  gr. 

X28-8; 

V 

Molecular 
weight 

1  Hydrogen 

•06926 

0° 

,, 

2 

2  Sodium 

•87 

1200°  —  1500° 

25-5 

23 

3  Nitrogen 

0-9713 

0° 

28-04 

28-02 

4  Oxygen 

rio6 
1-10563 

about  1400° 

0° 

31-94     \ 
31-92      J 

31-92 

°_        „         (ozone) 

1-658 

— 

47-86 

.     47-88 

7  Potassium 

i'3 

1200°  —  1500° 

377 

39^4 

8  Sulphur 

2-23 

860° 

64-4      ) 

J) 

2-24 

1040° 

64-6 

63-96 

10 

2-17 

about  1400° 

62-6      ) 

11 

2-93 

665° 

84-6 

p 

12 

6-62 

524° 

191-1 

191-88 

13  Zinc 

2-38 

about  1400° 

68-7 

64-9 

14  Chlorine 

2-45 

200° 

7073     ) 

15 

2'6l 

about  1000° 

75*35 

7074 

10 

2-44 

about  1200° 

7072     j 

17  Cadmium 

3-94 

about  1000° 

113-7 

112*1 

18  Phosphorus 

1!) 

4-35 
4-50 

about  1000° 

125-6      ) 
129-9      J 

I23-84 

20 

3-03 

1430° 

87-5 

p  6  1*92] 

21  Arsenic 

22 

IO"2 
IO-65 

860° 
644°--  668° 

294-5      \ 
307-4      } 

299-6 

23 

6-53                       1430° 

188-5 

[?  149-8] 

24  Bromine 

5'54 

100° 

1  59-9      / 

25 

100° 

I55'3      i 

r59"5 

26 

4'43 

about  1500° 

117-9 

? 

27  Selenion 

5-68 

about  1400° 

161*1 

157-6 

28 

6-37 

about  1000° 

183-9 

p 

29 

7-67 

860° 

221-4 

236-4 

30  Mercury 

6-96 

about  1000° 

200-93    j 

31 

32        I 

6-98 
7-03 

446" 
424° 

201-5      I 
203-0      [ 

199-8 

33 

67 

882° 

I93-4     J 

34  Iodine 

8-8 

250°—  450° 

254-0     S 

35 

872 

185° 

2517 

37 

8-70 
8-72 

447° 
about  1000° 

251-2 
251-7 

253-07 

38 
39 

5) 

8-84 
8-55 

250° 
665° 

255-2 
246-8     j 

40 

5-87 

about  1  1  00° 

169-4 

? 

41 

42  Tellurium 

476 
9-08 

about  1500° 
about  1400° 

262*1 

[?  126-53] 
255 

1  REGNAULT,  Compt.  rend.  20.  975.  2  SCOTT,  Proc.  R.  S.  E.  1888. 

3  REGNAULT,  loc.  cit.        4  V.  MEYER,  Ber.  12.  1426.        5  REGNAULT,  loc.  cit. 

M.  C.  3 


34  ATOMS   AND   MOLECULES.  [P.OOK  I. 

Mensching  and  Meyer  (Annalen,  240.  317)  have  obtained  values  for 
the  specific  gravity  of  antimony  gas  which  shew  that  at  1400°  —  1500° 
the  molecular  weight  of  this  element  is  less  than  Sb4. 

16  So  many  determinations  of  molecular  weights  of  com- 
pound gases  have  been  made  that  an  enumeration  of  all  the 
results  would  be  perplexing,  and  of  no  special  value.  The 
method  is  applicable  to  elements  and  compounds  alike.  The 
following  numbers  are  given  here  as  they  illustrate  a  point  of 
general  importance. 

Specific  gravities  of  certain  compound  gases. 

fSp.  gr.       5-08     4'QQ       4'3       3'6o     3-66 
Phosphorus  pcntachlonde...-LF 

\Temp.       180°      190     230       290     335 

fSp.  err.       2'8       2-4        2-03     1-83     i  -5 
N,,rogen,e,rox,dc  ............ 


Nitric  oxide  .....................  &.  gr.      ,'039        ,-039 

[Temp.       -70  1  6 

fSp.  gr.     13-8  1378 

Arsemous  oxide    ...............  I-.--  0 

[Temp.      570  1400 

From  these  numbers,  and  from  those  of  the  previous  table, 
it  is  apparent  that  the  specific  gravities  of  certain  elementary 
and  compound  gases  decrease  as  the  temperature  increases, 

6  SORET,  Compt.  rend.  61.  941  ;  and  64.  904.  7  SCOTT,  Proc.  R.  S.  E.  1888. 

s  and  9  DEVILLE  and  TROOST,  Compt.  rend.  56.  891.  10  V.  MEYER,  Ber.  12. 

r  1  12.  n  TROOST,  Compt.  rend.  95.  30.  12  DUMAS,  Ann.  Chim. 

Phys.  (2)  50.  170.  13  MENSCHING  and  MEYER,  Ber.  19.  3295.  14  LUD- 

WIG,  Ber.  1.  232.  15  V.  MEYER,  Ber.  13.  400.  16  Id.  do.  15.  2773 

(mean  of  5  experiments).  17  DEVILLE  and  TROOST,  Compt.  rend.  49.  239. 

is  »nd  w  /,/_  fa  56>  891.  20  MENSCHING  and  MEYER,  Annalen,  240.  317. 

21  D.  and  T.  loc.  cit.  **  MITSCHERLICH,  Annalen,  12.  159.  23  MEN- 

SCHING and  MEYER,  Annalen,  240.  317.  24  MITSCHERLICH,  loc.  cit. 

25  V.  MEYER,  Ber.  13.  406.        26  CRAFTS,  Compt.  rend.  90.  183.        -1-  "8and  w  DE- 
VILLE and  TROOST,  loc.  cit.  30  V.  MEYER,  Ber.  13.  1107  and  mo  (mean 

of  6  experiments).  31  DUMAS,  Ann.  Chim.  Phys.  (2)  33.  337.  32  MIT- 

SCHERLICH, loc.  cit.  33  BINEAU,  Compt.  rend.  49.  799.  34  V.  MEYER, 

and  MEIER  and  CRAFTS,  Ber.  13.  868  (mean  of  7  experiments).  35  DUMAS, 

loc.  cit.  36»nd37  DEVILLE  and  TROOST,  loc.  cit.  38  V.  MEYER,  Ber. 

13.  396.  39  TROOST,  Compt.  rend.  95.  30.  40  V.  MEYER,  Ber.  13.  1115. 

41  Id.  do.  13.  to  10.  42  DEVILLE  and  TROOST,  loc.  cit. 

Note  to  preceding  table.  The  expression  '  specific  gravity  of  a  gas  '  will  be 
employed  to  denote  the  specific  gravity  referred  to  air  as  unity  :  the  expression 
'  vapour  density  of  a  body  '  to  denote  the  specific  gravity  of  a  body  in  the  gaseous 
state  referred  to  hydrogen  as  unity. 


CHAP.  I.  §§l6-I7]     SPECIFIC   GRAVITIES   OF   VAPOURS.  35 

while  in  the  case  of  other  gases  the  density  is  practically 
independent  of  the  temperature ;  a  limiting  value  is  however 
generally  found  for  the  specific  gravity  of  a  gas. 

It  would  therefore  appear  that  a  chemical  substance  may 
have  more  than  one  molecular  weight;  but  if  the  molecule  is  the 
smallest  part  of  a  substance  which  exhibits  the  characteristic 
properties  of  that  substance,  this  is  equivalent  to  saying  that 
certain  substances  when  heated  may  pass  through  a  succession 
of  changes,  each  phase  being  marked  by  the  existence  of  a 
distinct  kind  of  matter.  More  accurate  experiment  has  shewn 
that  the  vapours  of  phosphorus  pentachloride  and  nitrogen 
tetroxide,  at  high  temperatures,  are  mixtures  of  phosphorus 
pentachloride  and  trichloride,  and  chlorine,  and  of  nitrogen 
tetroxide  and  nitrogen  dioxide  (N2O4  and  NOJ,  respectively, 
so  that  at  these  temperatures  we  have  to  deal  not  with 
homogeneous  vapours,  but  with  mixtures  of  different  gases 
varying  in  composition  at  different  moments.  The  con- 
nexion existing  between  temperature  and  the  densities  of 
gaseous  elements  and  compounds  will  be  examined  in  more 
detail  in  a  future  chapter1  (see  Book  II.). 

The  practical  outcome  of  these  considerations  is  that  in 
determining  a  molecular  weight  the  gas  must  be  proved  to 
be  really  a  homogeneous  substance,  and  not  a  mixture  pro- 
duced by  the  decomposing  action  of  heat  on  the  original  sub- 
stance ;  and,  further,  that  the  value  obtained  for  the  specific 
gravity  must  be  constant  throughout  a  considerable  range  of 
temperature. 

[7  In  determining  the  specific  gravity  of  a  gas,  especially 
if  at  a  somewhat  high  temperature,  many  sources  of  error 
are  present ;  the  result  cannot  therefore  be  more  than  mode- 
rately accurate2.  But  experimental  errors  are  more  easily 

1  Avogadro's  law  may  he  deduced  from  the  molecular  theory  of  matter,  but 
inasmuch  as  this  theory  is  based  upon  more  or  less  inexact  hypotheses,  and  is  as 
yet  but  in  an  early  stage  of  development,  inasmuch  also  as  the  deductions  made 
from  it  concerning  gaseous  laws  are  strictly  applicable  only  to  '  perfect  gases,"  it 
follows  that  Avogadro's  law  cannot  be  regarded,  at  present,  as  absolutely  true. 
The  laws  of  Boyle  and  of  Charles,  which  are  also  deducible  from  the  molecular 
theory,  do  not  give  a  complete  account  of  the  relations  of  gases  to  temperature  and 
pressure. 

-  Dumas'  method  for  determining  vapour  densities  is  described  in  Ann.  Chim. 

3—2 


36  ATOMS   AND   MOLECULES.  [BOOK  I. 

avoided  in  the  determination  of  the  mass  of  an  element  which 
combines  with  one  part  by  weight  of  hydrogen,  7-98  parts  by 
weight  of  oxygen,  or  3  5 '37  parts  by  weight  of  chlorine.  Now, 
if  this  mass  is  called  the  combining  iveight  of  an  element, 
it  is  evident  that  the  molecular  weight  of  an  element  must 
be  equal  to,  or  a  multiple  of,  its  combining  weight,  and  the 
molecular  weight  of  a  compound  must  be  equal  to  the  sum, 
or  to  a  multiple  of  the  sum,  of  the  combining  weights  of  its 
constituent  elements.  Hence  if  the  combining  weight,  and 
the  specific  gravity  in  the  gaseous  state,  of  an  element  are 
carefully  determined,  we  have  the  necessary  data  for  an 
accurate  determination  of  the  molecular  weight  of  that  element; 
the  combining  weight  being  an  accurately  determined  num- 
ber, and  the  specific  gravity  deciding  what  multiple  of  that 
number  represents  the  molecular  weight.  So  also  the  data 
required  for  an  accurate  determination  of  the  molecular 
weight  of  a  compound  are;  the  combining  weights  of  the 
constituent  elements,  and  the  specific  gravity  of  the  com- 
pound in  the  state  of  gas.  Thus  Regnault  found  for  the 


Phys.  [2]  33.  337;  Gay  Lussac's  in  Biot's  Traitt  de  Phys.  1.  291;  Hofmann's  in 
Ber.  1.  198;  and  Victor  Meyer's  in  Ber.  11.  1868  and  2253.  For  criticisms  on, 
and  modifications  of,  Meyer's  method  see  Ber.  12.  609  and  1112:  13.  401,  851,  991, 
1079,  1185,  and  2019:  14.  1727:  and  15.  137,  1161  and  2775:  (in  the  last  paper  by 
V.  Meyer  [Ber.  15.  2775]  will  be  found  an  interesting  and  valuable  criticism  of  the 
various  methods  for  finding  the  Sp.  Grs.  of  gases).  See  also  Ber.  16.  1051;  19. 
1 86 1 ;  also  C.  S.  Journal  Trans,  for  1880.  491.  Modifications  of  Dumas'  method 
are  described  by  Bunsen,  see  Gasometrische  Methoden,  2nd  ed.  (1877),  p.  172:  also 
by  Petterson  and  Ekstrand,  Ber.  13.  1191  :  and  especially  by  Pawlewski,  Ber.  16. 
1293.  Thorpe  [C.  S.  Jotirnal  Trans,  for  1880.  147—150]  has  described  a  very 
complete  method  based  on  Hofmann's  process.  V.  Meyer  [Ber.  9.  1260:  and  10. 
2068]  has  described  a  method  based  on  the  displacement  of  mercury.  In  Wied. ' 
Ann.  22.  465  and  493,  von  Klobukow  describes  two  processes  for  determining 
vapour  densities  with  great  accuracy ;  one  is  adapted  for  bodies  with  low  boiling 
points,  the  other  for  bodies  which  boil  at  high  temperatures.  La  Coste  (Ber.  18. 
2122)  describes  a  modification  of  V.  Meyer's  apparatus  whereby  the  vapour 
densities  of  easily  decomposable  compounds  may  be  determined  at  low  tempera- 
tures and  under  very  small  pressures.  A  modification  of  V.  Meyer's  apparatus, 
by  which  a  vapour  density  and  the  exact  temperature  of  observation  can  be  simul- 
taneously determined,  is  described  by  Nilson  and  Pettersson  in  J.  fiir  prakt. 
Chem.  [2]  33.  r.  See  also  Schall,  Ber.  20.  1433.  Malfatti  and  Schoop  (Zeitschr. 
f.  physikal.  Chemie,  1.  159)  describe  an  apparatus  for  determining  vapour  densities 
under  small  pressures. 


CHAP.  I.  §§  I7-I8]         ATOMIC   WEIGHTS.  37 

specific  gravity  of  chlorine  the  number  2*44 ;  this  multiplied 
into  28*87  gives  70*44.  The  combining  weight  of  chlorine  as 
most  carefully  determined  by  Stas  is  35'37:  now  35'37  x  2 
=  7074,  which  is  very  nearly  equal  to  the  molecular  weight 
calculated  from  Regnault's  numbers ;  hence  7074  is  taken  to 
be  the  molecular  weight  of  chlorine.  Again,  Thomson  found 
the  specific  gravity  of  marsh  gas  to  be  O'557,  which  multiplied 
into  28*87  gives  16*1  as  approximately  the  molecular  weight 
of  this  compound  :  the  combining  weight  of  carbon  is  2*99 
(H  =  i),  and  in  marsh  gas  carbon  and  hydrogen  are  united  in 
the  proportion  of  2*99  to  I  ;  hence  the  molecular  weight  of 
this  gas  is  3*99  or  a  multiple  thereof.  But  3*99  x  4=  15*96 ; 
therefore  the  molecular  weight  of  marsh  gas  is  taken  to  be 
15-96. 

The  numbers  in  column  V  of  the  table  on  p.  33  represent 
the  molecular  weights  of  the  various  elements  found  by  the 
method  of  specific  gravity  aided  by  determinations  of  the 
combining  weights  of  the  elements  in  question. 
L8  Facts  have  already  been  mentioned  which  on  the  as- 
sumption of  the  truth  of  Avogadro's  law  oblige  us  to 
conclude  that  in  certain  chemical  reactions  the  molecules  of 
the  reacting  elementary  bodies  undergo  subdivision  ;  indeed 
we  are  forced  to  the  conclusion  that  the  greater  number  of 
the  molecules  of  those  elements  which  have  been  gasified 
are  not  homogeneous  but  are  built  up  of  smaller  parts1. 
These  parts  of  molecules,  or  atoms,  are  the  ultimate  portions 
of  matter  with  which  we  have  at  present  to  deal  in  chemistry. 
Now  it  is  evident  that  the  molecule  of  an  element  must  be 
composed  of  at  least  two  atoms,  unless  indeed  the  atom  and 
molecule  should  be  identical;  and  that  the  molecule  of  a 
compound  must  be  composed  of  at  least  one  atom  of  each 
of  its  constituent  elements.  Therefore  if  we  determine  the 
smallest  mass  of  an  element  in  the  molecule  of  any  compound 
thereof,  we  shall  have  determined  the  maximum  atomic  weight 
of  the  element  in  question. 

Hence  we  arrive  at  the  following  definition. 

1  Reactions  are  known  in  which  it  is  not  necessary  to  assume  that  subdivision 
of  elementary  molecules  occurs,  e.g. 

Hg  +  Cls  =  HgCl,, 
Volumes   2        2  form  2. 


38  ATOMS   AND   MOLECULES.  [BOOK  I. 

The  maximum  atomic  weight  of  an  element  is  the 
smallest  mass,  in  terms  of  hydrogen  as  unity,  of  that  element 
which  combines  with  other  elements  to  form  a  gaseous  molecule. 

Molecular  weight  has  been  already  defined  as  the  weight  of 
two  volumes  of  any  gas  referred  to  the  weight  of  two  volumes 
of  hydrogen ;  hence  the  data  which  must  be  obtained  before 
the  maximum  atomic  weight  of  an  element  can  be  determined 
are,  (i)  the  specific  gravities  of  several  gaseous  compounds  of 
the  element  in  question,  and  (2)  careful  analyses  of  these 
compounds. 

Suppose  it  is  required  to  determine  the  maximum  atomic 
weight  of  oxygen,  such  data  as  are  indicated  in  the  following 
table  are  obtained. 

Data  for  determining  maximum  atomic  weiglit  of  oxygen. 


Weight  of 

2  volumes,  as 

Name  of  compound 

gas,  referred  to 

Analysis  of  these  2  volumes 

hydrogen,  i.  e. 

molecular  weight 

Water 

17-99 

1  5  '96  oxygen  +      2     hydrogen 

Carbonous  oxide 

27-96 

!5'96       ,,       +    ii  '97  carbon 

Carbonic  dioxide 

44'  1  5 

31-92       „       +    11-97       „ 

Nitrous  oxide 

43'9 

J5'96        n       +   28*02  nitrogen 

Methylic  alcohol 

32'3 

(15-96       „       +    1  1-97     carbon 
|                          +     4      hydrogen 

Methyl  nitrate 
Nitric  oxide 

76-2 
30-0 

}  47'88       „       +11  -97  carbon 
'  +3hydrogen+    14-01  nitrogen 
15-96  oxygen  +    14-01         „ 

Sulphurous  oxide 

64-9 

31-92       „        +    31-98  sulphur 

Sulphuric  oxide 

86-9 

47-88       „        +   31-98         „ 

Phosphorus  oxychloride 

155*9 

'5  '96        „        +   30-96  phosphorus 

+  106-11  chlorine 

Osmium  tetroxide 

257 

63-84       „        +198*6    osmium 

If  the  smallest  mass  of  hydrogen  found  in  a  molecule  of  any 
compound  of  that  element  is  called  one  part  by  weight,  then 
in  no  molecule  of  any  of  the  compounds  in  this  table  is  there 
less  than  15 '96  parts  by  weight  of  oxygen;  this  number  is 
therefore  adopted  as  the  maximum  atomic  weight  of  oxygen. 
19  The  following  table  (taken  for  the  most  part  from  Lothar 
Meyer's  Die  modernen  Theorien  der  Chemic)  contains  the 
most  important  data  hitherto  accumulated  for  determining  the 
maximum  atomic  weights  of  the  elements  by  the  application 
of  Avogadro's  law. 


CHAP.  I.  §  19]    MOLECULAR  AND  ATOMIC  WEIGHTS. 


39 


40 


ATOMS   AND   MOLECULES. 


[BOOK  i. 


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CHAP.  I.  §  Ip]   MOLECULAR  AND  ATOMIC  WKHHITS. 
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42 


ATOMS   AND   MOLECULES.  [BOOK  I. 


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CHAP.  I.  §  19]    MOLECULAR  AND  ATOMIC  WEIGHTS. 


43 


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44  ATOMS   AND   MOLECULES.  [BOOK  I. 

Notes  to  the  preceding  Table. 

I  The  density  of  hydrofluoric  acid  was  determined  indirectly  by  Gore  (Phil. 
Trans,  for  1869.  173)  at  100°.     Mallet  (Amer.  Chem.  Journal  3.  189)  by  directly 
weighing  i  litre  of  the  gas  at  30°  found  the  specific  gravity  to  be   1-42,  which 
gives  a  molecular  weight  of  41-02.     The  molecular  weight  of  this  gas  therefore 
decreases  as  temperature  increases. 

2»nd3  indirectly  determined  by  Bineau  (Ann.  Chim.  Phys.  [2]  68.  424);  two 
volumes  of  each  hydride  when  decomposed  by  metal  yielded  2  vols.  of  hydrogen, 
78  parts  by  weight  of  selenion  in  one  case,  and  128  parts  by  weight  of  tellurium 
in  the  other  case,  being  produced. 

34  Michaelis,  Ber.  20.  1780,  and  2488.     Temp.  abt.  450°. 

4  Potassium  iodide  was  vaporised  at  about  1300°  by  means  of  a  new  apparatus 
described  by  Mensching  and  Meyer  (s.  Zeitschr.f. physikal.  Chemie,  1.  157). 

5  Determined  at  1200°— 1500°  by  Scott;  Proc.  R.  S.  E.  1887. 

6  At  a  temperature  slightly  above  its  boiling  point  the  specific  gravity  of 
gaseous  stannous  chloride  points  to  the  molecular  weight  377;  but  at  200°  higher 
the  specific  gravity  is  as  given  in  the  table ;  this  gas  therefore,  like  hydrofluoric 
acid,  has  two  molecular  weights:  see  Meyer  and  Ziiblin  (Ber.  13.  811). 

7  GeCl4,  GeI4,  and  GeS  have  been  gasified  by  Nilson  and  Pettersson  (Zeit.f. 
physikal.  Chemie,  1.  27). 

8  Kriiss  and  Nilson,  Ber.  20.  1671.     Temp.  abt.  1200°. 

9  See  Nilson  and  Pettersson,  Ber.  17.  987;  also  J.fiir prakt.  Chem.  [2]  33.  i; 
and  Humpidge,  Proc.  R.  S.  38.  188. 

10  There  is  some  doubt  whether  the  vapour  of  mercurous  chloride  does  or  does 
not  contain  mercury  and  mercuric  chloride:  the  number  in  the  table  is  from  a 
paper  by  Fileti,  who  states  that  by  vaporising  a  mixture  of  the  two  chlorides  of 
mercury,  the  protochloride  remains  undissociated  (see  abstract  of  Fileti's  paper  in 
C.  S.  Journal  Abstracts  for  1882.  466). 

II  Nilson  and  Pettersson  (Zeitschr.f.  physikal.  Chemie,  1.  459)  have  found  that 
the  sp.  gr.  of  gaseous  aluminium  chloride  at  800° — 1200°  agrees  with  the  formula 
A1C13;  at  400°  or  so  it  agrees  with  the  formula  A12C16.     Odling  (Phil.  Mag.  [4] 
29.  316)  gave  the  specific  gravity  of  aluminium  trimethide  at  temperatures  above 
200°  as  2  '5,  and  at  1 30°  as  5  'o ;  but  it  is  undecided  whether  the  gas  at  200°  was 
homogeneous  or  a  mixture  of  the  products  of  decomposition  by  heat  of  molecules 
existing  at  lower  temperatures  (see  Wanklyn  loc.  cit.  313,  and  Williamson  do.  395). 
If  the  gas  at  200°  was  really  homogeneous,  we  should  have  2-5  x  28-87  =  72-5  as 
the  molecular  weight  of  aluminium  trimethide ;  and  this  quantity  of  the  gas  con- 
tains 27-02  aluminium +  35-91  carbon  +  9  hydrogen  (=71-93).     Chromium  hexa- 

Jluoride  (CrF6)  is  frequently  mentioned  in  text-books  as  a  gaseous  compound  of 
chromium ;  the  evidence  in  favour  of  the  existence  of  a  definite  fluoride  of 
chromium  is  meagre ;  and  no  determinations  of  its  density  (if  it  exists)  have  been 
made:  see  Unverdorben  (Pogg.  Ann.  1.  311).  According  to  Oliveri  (Gaz.  16,  218) 
the  supposed  hexafluoride  is  really  an  oxyfluoride,  of  chromium,  and  has  the  com- 
position CrO2F2. 

12  V.  Meyer  (Ber.  17.  1335)  has  obtained  results  which  seem  to  shew  that 
gaseous  ferrous  chloride  at  moderate  temperatures  consists  chiefly  of  molecules  having 
the  composition  Fe2Cl4,  and  at  higher  temperatures  chiefly  of  molecules  of  FeCl2. 

13  At  450°  the  sp.  gr.  of  the  vapour  of  gallic  chloride  is  7-8,  and  at  the  same 


CHAP.  I.  §  2O]    MOLECULAR  AND  ATOMIC  WEIGHTS. 


45 


temperature  in  presence  of  an  indifferent  gas  acting  as  diluent,  it  is  6*6 :  the  gas 
dissociates  under  these  conditions.  (See  Lecoq  de  Boisbaudran,  Comft.  rend.  93. 
294,  329  and  815.) 

The  maximum  atomic  weights  deduced  from  these  data 
may  in  many  cases  be  regarded  with  a  large  degree  of  proba- 
bility as  the  true  atomic  weights  of  the  elements.  The 
greater  the  number  of  gaseous  compounds  of  an  element 
analysed,  the  greater  is  the  probability  that  the  number  which 
represents  the  smallest  mass  of  that  element  in  two  volumes, 
i.e.  in  a  gaseous  molecule,  of  any  of  these  compounds  is  the 
true  atomic  weight  of  the  element. 

20  When  the  atomic  and  molecular  weights  of  an  element 
are  known,  the  atomicity  of  the  molecule,  i.e.  the  number  of 
atoms  in  the  molecule,  is  known. 

In  the  following  table  the  molecules  of  the  elements,  so 
far  as  the  relative  weights  of  these  have  been  determined  by 
the  method  founded  on  Avogadro's  law,  are  classified  in 
accordance  with  their  atomicity. 

Atomicity  of  Elementary  Molecules1. 


Monatomic 

Diatomic 

Triatomic 

Tetratomic 

Hexatomic 

Sodium 
Potassium 

Hydrogen 
Chlorine 

Oxygen  (ozone) 
Selenion 

Phosphorus 
Arsenic 

Sulphur 
(450°  to 

Zinc                     Bromine 
Cadmium            Iodine 

(700°  to  800°) 

(to  near  a 
white  heat) 

about  550°, 

Mercury            '     (200°  to  about 

Iodine                   1000°) 

(at  about  1  500°)     Oxygen 
(?  Bromine  at   '  Sulphur 

about  1800°)         (at  800°  and 

upwards) 

Selenion 

(at  1200°  and 

upwards) 

Tellurium 

Nitrogen 

Phos-     )   (at 

phorus>white 

Arsenic)  heat) 

1  This  table  shews  that  many  elementary  gases  have  complex  structures ; 
hence  arise  difficulties  in  forming  accurate  physical  conceptions  of  actions  and 
reactions  among  the  parts  of  these  structures.  This  will  be  again  referred  to  when 
dealing  with  atomic  heats  (see  p.  67). 


46  ATOMS   AND   MOLECULES.  [BOOK  I. 

The  molecules  of  several  elements  in  this  table  are 
diatomic,  but  inasmuch  as  the  molecular  and  atomic  weights 
of  only  1 6  elements  have  been  determined  it  is  impossible 
to  say  whether  a  majority  of  all  the  elementary  molecules 
are  composed  each  of  two  atoms.  Six,  of  the  sixteen, 
elements  in  the  table  have  more  than  one  molecular  weight; 
of  the  remaining  ten,  five  are  monatomic  and  five  are 
diatomic. 

The  table  contains  five  well-defined  metals,  sodium,  potas- 
sium, zinc,  cadmium,  and  mercury  ;  the  molecules  of  these 
elements  are  monatomic,  and  hence  are  of  a  simpler  structure 
than  the  molecules  of  the  distinctly  nonmetallic  elements. 
21  Chemical  formulae  for  the  most  part  profess  to  repre- 
sent not  only  the  elementary  composition,  but  also  the  rela- 
tive weights  of  the  molecules,  of  the  bodies  formulated  :  but 
unless  some  method  for  determining  molecular  weights  other 
than  that  founded  on  Avogadro's  law  is  adopted,  it  is  evident 
from  the  data  in  the  table  on  pp.  39 — 43  that  the  majority  of 
the  formulae  employed  in  mineral  chemistry  cannot  certainly 
be  regarded  as  molecular  formulae.  Thus  analysis  shews  that 
17-96  parts  by  weight  of  water  are  composed  of  15 '96  parts 
of  oxygen  and  2.  parts  of  hydrogen  ;  analysis  also  shews  that 
58*37  parts  by  weight  of  sodium  chloride  are  composed  of 
23  parts  of  sodium  and  35'3/  parts  of  chlorine.  The  specific 
gravity  of  water  vapour  shews  that  the  molecular  weight  of 
this  compound  is  about  18,  hence — assuming  the  atomic 
weight  of  oxygen  to  be  1 5^96 — the  molecular  formula  is  written 
H2O  ( 1 7-96).  But  no  determination  of  the  specific  gravity  of 
sodium  chloride  vapour  has  yet  been  made ;  hence  the  mole- 
cular weight  may  be  about  59,  or  it  may  be  a  multiple  of  this 
number  (assuming  the  atomic  weights  of  sodium  and  chlorine 
to  be  known),  and  hence  the  formula  NaCl  (58'37)  is  not 
necessarily  molecular,  and  is  therefore  not  strictly  comparable 
with  the  formula  H2O. 

Even  if  a  formula  does  express  the  relative  weight  of  the 
molecule  of  the  body  formulated  it  is  well  to  remember  that 
it  is  the  weight  of  the  gaseous  molecule  which  is  thus  ex- 
pressed ;  the  formula  does  not  necessarily  also  represent  the 


CHAP.  I.  §2l]     FORMULA   OF   GASES   AND   SOLIDS.  47 

relative  weight  of  the  molecule  of  the  same  body  when 
solid  :  indeed  the  definition  of  molecule  (p.  26)  is  applicable 
to  gases  only. 

As  a  general  rule,  the  melting  and  boiling  points  of  bodies 
with  large  molecular  weights  are  high :  thus  in  any  homologous 
series  of  hydrocarbons  the  boiling  and  melting  points  increase 
with  increase  of  molecular  weight1  ;  the  same  connexion 
between  these  constants  is  noticed  in  many  series  of  oxides, 
e.g.  the  oxides  of  nitrogen2.  It  would  therefore  appear  pro- 
bable that  the  molecular  weight  of  a  solid,  using  the  term 
molecular  weight  in  a  wide  sense,  is  greater  than  that  of  the 
same  substance  when  in  the  state  of  gas.  So  also,  as  a  rule, 
the  action  of  heat  is  to  produce  molecules  of  less,  from  those 
of  greater,  weight :  thus  NaO4  exists  at  low  temperatures,  but 
becomes  NOa  when  heated  (see  numbers  on  p.  34);  so  S6 
exists  at  500°,  but  S2  at  1000° ;  at  temperatures  above  300° 
the  molecule  O3  decomposes  into  O2.  Reactions  are  known 
in  which  heat  appears  to  favour  the  production  of  particles  of 
greater  weight  and  complexity  than  those  previously  existing; 
but  these  more  complex  particles  generally  mark  intermediate 
stages  towards  the  formation  of  less  complex  and  compara- 
tively lighter  particles.  Thus  the  action  of  heat  on  sodium- 
hydrogen  sulphate  is  generally  formulated  in  two  stages,  (i) 
2NaHS04=Na2S207+H20;  (2)  Na2S2O7  =  Na8SO4  +  SO3:  so 
also  when  mercuric  cyanide  is  decomposed  by  heat,  molecules 
of  cyanogen  are  produced  having  the  formula  wCN  where 
11  >  2,  but  at  800° — 900°  these  are  separated  into  the  lighter 
molecules  C2N2:  again,  lead  monoxide,  wPbO,  when  heated 
forms  the  heavier  oxide  «Pb3O4:  &c.  In  many  of  these  cases 
however  we  are  not  certain  that  the  formulae  employed 
represent  the  relative  weights  of  true  molecules. 

The  physical  phenomena  presented  by  liquids  and  solids 
cannot  be  expressed  by  such  comparatively  simple  generali- 
sations as  those  which  express  the  properties  of  gases;  the 

1  Thus,         C4H10,   C5H12,    C6H14,   C7H,6,    C8H18,   C9HW,   C^H^  &c. 
B.  P.=  i°          38°         70°          99°         124°        148°         167°   &c. 

2  Thus,     NO  N2O  N2O3         N.2O4         N2O5 
gaseous  at  -  110°,  B.P.  =  -88°,  about  -20°,      42°.      M.P.  =  3O°. 


48 


ATOMS   AND   MOLECULES. 


[BOOK  i. 


molecular  phenomena  of  the  former  classes  of  bodies  are 
evidently  more  complex  than  those  of  the  latter  class.  Great 
caution  must  therefore  be  used  in  applying  deductions  made 
from  the  study  of  the  molecular  phenomena  of  gases  to 
solid  or  liquid  bodies1. 

22  The  following  table  gathers  together  the  results  of  obser- 
vations recorded  in  the  table  on  pp.  39 — 43,  so  far  as  regards 
the  maximum  atomic  weights  of  elements  determined  by  the 
application  of  Avogadro's  law. 

Maximum  atomic  weights  of  elements.     (AVOGADRO'S  law.) 


Name 

Maximum 
atomic 
weight 

Name 

Maximum 
atomic 
weight 

Name 

Maximum 
atomic 
weight 

Hydrogen 

I 

Manganese 

55 

Antimony          120 

Beryllium 

9'I 

Zinc 

64-9 

Tellurium 

125 

Boron 

IQ'95 

Germanium 

72'3 

Iodine                I26'53 

Carbon 

II'97 

Arsenic 

74'9 

[Copper             I26-8]2 

Nitrogen 

I4-OI 

Selenion 

78-8 

Caesium              132-7 

Oxygen 

15-96 

Bromine 

7975 

[Gallium            138]* 

Fluorine 

I9-I 

Rubidium 

85-2 

Tantalum          182 

Aluminium 

27-02 

Zirconium 

90 

Tungsten        j   183-6 

Silicon 

28 

Niobium 

94 

Osmium 

193  (?) 

Phosphorus 
Sulphur 

30-96 
31-98 

Molybdenum 
Silver 

95-8 
107-66 

Mercury             !99'8 
Thallium           203-6 

Chlorine 

35'37 

[Iron 

in-8]2 

Lead                  206-4 

Potassium           39'O4 

Cadmium 

112 

Bismuth            208 

Titanium             48 

Indium 

II3-4 

Thorium 

231-87 

Vanadium 

51-2 

Tin 

II7-8 

Uranium 

240 

Chromium 

52-4 

About  two-thirds  of  the  known  elements  are  found  in  this 
table. 

Some  method  other  than  that  based  on  the  determination 

of  the  specific  gravities  of  gaseous  compounds  must  if  possible 

be  discovered  for  finding  the  atomic  weights  of  the  elements. 

23        In  his  New  System  of  Chemical  Philosophy*  (pp.  70 — 75), 

Dalton    discusses    hypotheses    regarding   the    quantities    of 

1  The  comparison  of  the  molecular  phenomena  of  gases  with  those  of  solids 
and  liquids  will  be  considered  more  fully  in  a  future  chapter.     See  Book  ii. 
Chap.  iv. 

2  Especial  reference  will  be  made  to   the   elements   in   brackets   in   a   later 
paragraph :  see  p.  60. 

3  Published  in  1 808. 


CHAP.  I.  §§  22-23]  ATOMIC   HEATS.  49 

heat  contained  In  various  elastic  fluids,  and  decides  in  favour 
of  that  which  asserts  that, 

"  The  quantity  of  heat  belonging  to  the  ultimate  particles  of  all  elastic 
fluids  must  be  the  same  under  the  same  pressure  and  temperature." 

From  this  Dalton  deduced  the  corollary, 

"The  specific  heats  of  equal  weights  of  any  two  elastic  fluids  are 
inversely  as  the  weights  of  their  atoms  or  molecules." 

The  values  of  very  few  specific  heats  had  been  determined 
when  Dalton  wrote,  and  therefore  he  did  not  possess  data 
sufficient  to  test  the  justness  of  his  general  principle.  Dalton 
calculated  the  theoretical  specific  heats  of  various  gases  by 
the  aid  of  the  above  corollary,  employing  atomic  weights  de- 
termined by  himself.  Regarding  the  table  of  numbers  thus 
obtained  he  remarks, 

"  Upon  the  whole  there  is  not  any  established  fact  in  regard  to  the 
specific  heat  of  bodies,  whether  elastic  or  fluid,  that  is  repugnant  to  the 
above  table  so  far  as  I  know  ;  and  it  is  to  be  hoped  that  some  principle 
analogous  to  the  one  here  adopted  may  soon  be  extended  to  solid  and 
liquid  bodies  in  general." 

In  1819  a  paper  by  Petit  and  Dulong  appeared  in  the 
Annales  de  Chimie  et  de  Physique  [10.  395],  containing  the  re- 
sults of  determinations  of  the  specific  heats  of  thirteen  solid 
elements;  viz.  copper,  gold,  iron,  lead,  nickel,  platinum, 
sulphur,  tin,  zinc,  bismuth,  cobalt,  silver,  and  tellurium.  A 
nearly  constant  product  was  obtained  by  multiplying  the 
specific  heats  of  the  nine  elements  from  copper  to  zinc,  in  this 
list,  by  the  then  generally  accepted  atomic  weights  of  these 
elements,  and  the  specific  heat  of  bismuth,  cobalt,  silver,  and 
tellurium,  by  a  sub-multiple  of  the  accepted  atomic  weight 
of  each  of  these  elements.  Generalising  from  these  results 
the  French  physicists -concluded  that  "the  atoms  of  all  the 
simple  bodies  have  exactly  the  same  capacity  for  heat" 

The  introduction  of  more  accurate  methods  for  determin- 
ing specific  heats  has  necessitated  considerable  alterations  in 
many  of  the  numbers  to  be  found  in  the  original  paper  of 
Petit  and  Dulong,  nevertheless  their  general  conclusion  re- 
mains, although  it  cannot  now  be  stated  in  terms  quite  so 
absolute  as  those  used  by  its  promulgators. 

M.  C.  4 


50  ATOMS   AND   MOLECULES.  [BOOK  I. 

24  In  1831  F.  Neumann1  published  determinations  of  the 
specific  heats  of  various  solid  compounds,  chiefly  of  natur- 
ally occurring  minerals,  and  deduced  the  general  statement: — 
"  The  amounts  of  cJtemically  similar  compounds  expressed  by 
their  formulce  possess  equal  specific  heats." 

A  few  years  later  (1833 — 4)  Avogadro2  detailed  measure- 
ments of  the  specific  heat  of  carbon,  and  of  various  com- 
pound substances,  and  drew  certain  general  conclusions  there- 
from ;  he  spoke  of  those  atomic  weights  which  were  deduced 
from  measurements  of  specific  heats  as  the  weights  of  thermal 
atoms  (atomes  thermiques]. 

R.  Hermann3  made  a  number  of  determinations  of  specific 
heats,  and  from  these  deduced  the  combining  weights  of 
several  elements.  The  weights  thus  obtained  were  in  some 
cases  different  from  the  Berzelian  weights  then  in  general  use. 
Hermann  supposed  that  the  specific  heat  of  certain  elements, 
e.g.  sulphur  and  oxygen,  varies  according  as  the  element  is 
in  the  free  state  or  in  combination  with  other  elements. 

Regnault4,  in  a  series  of  classical  memoirs,  added  much  to 
our  knowledge  of  specific  heats,  and  gave  a  general  confirma- 
tion to  the  laws  of  Dulong  and  Petit,  and  Neumann.  He 
arranged  a  table  of  so-called  thermo-atomic  weights,  as  follows  : 
Regnaulfs  Thermo-atomic  weights.  [See  KOPP5.] 

Al  =137 

Sb  =  61 

As  =37-5 

Ba  =68-5 

Bi  =105 

B    =10-9 

Br  =40 

Cd=s6 

Ca=2o 

C    =  12 

Cl  =1775 

1  P°SS-  Ann.  23.  i.     Neumann  measured  the  specific  heats  of  8  carbonates, 
4  sulphates,  4  sulphides,  5  oxides  of  the  type  MO,  and  3  of  the  type  M2O3. 

2  Published  in  condensed  form  in  Ann.  Chim.  Phys.  [2]  55.  80:  and  57.  113. 

3  Noweaux  Mt 'moires  de  la  Socittt  Imptriale  des  Naturalistes  de  Moscou  (1834). 
3.  137. 

4  Ann.  Chim.  Phys.  [2]  63.  5.  [3]  1.  129:  9.  322:  26.  261  and  268:  38.  129: 
46.  257:  63.  5.  5  Annakn,  Supplbd.  3.  i  and  289. 


Cr  =26-1 

Mn  =  27'5 

Se  =397 

Co  =29-4 

Hg  =  ioo 

Ag=54 

Cu  =317 

Mo  =  48 

Na  =  ii'5 

F    =9'5 

Ni  =29-4 

Sr  =43-8 

Au  =98-5 

N    =7 

S     =16 

I     =63-5 

Os  =99-6 

Te=64 

Ir    =99 

Pd=53-3 

Tl    =102 

Fe  =28 

P    =15-5 

Sn=S9 

Li  =3-5 

Pt  =987 

Ti  =25 

Pb=  103-5 

K    =19-5 

W  =92 

Mg=I2 

Rh=52-2 

Zn  =32-6 

CH.  I.  §§  24-25]    GARNIER-CANNIZZARO  GENERALISATION.    5  I 

Gamier6  (in  1852)  further  generalised  the  relations  between 
the  formulae  and  the  specific  heats  of  solid  compounds ;  and 
Cannizzaro7  somewhat  advanced  the  generalisation  of  Gamier. 

The  Garnier-Cannizzaro  generalisation  may  be  stated 
thus  :— 

A  C 

— =  constant  (about  6-4)  ; 

where  A  =  the  formula-weight  of  a  compound,  C  =  the  specific 
heat  of  the  same  compound,  and  n  =  the  number  of  elementary 
atoms  in  the  formula  of  the  compound. 

15  Kopp8  has  gathered  together  most  of  the  trustworthy 
results  of  specific  heat  determinations,  and  added  many  of 
his  own,  besides  discussing  the  whole  subject  in  detail. 

Table  of  Specific  Heats  of  the  Elements9. 


Name 

s& 

Temp. 

Atomic 
weight 

Sp.  ht. 
X  at  wt. 

Observer 

Lithium 

0-941 

7-01 

6-6 

Rg. 

1  Beryllium 
2  Boron 

0-62 
?o-5 

450°  to  500° 
about  iooo°? 

I0'9 

5-6 
5'5 

He. 
Wb. 

3  Carbon 

0-463 

980° 

11-97 

5'5 

Wb. 

Sodium 

0-293 

-34°  to  +7° 

23 

6-7 

Rg- 

Magnesium 

0-245 

24 

5'9 

Kp. 

M 

0-25 

„ 

6-0 

Rg. 

Aluminium 

0-202 

27-02 

5-5 

Kp. 

99 

0-214 

>9 

I'8 

Rg. 

>? 

0-225 

H 

6-r 

Mt. 

4  Silicon 

0-203 

232° 

28-3 

5-8 

Wb. 

Phosphorus  (cryst.) 

0-174 

-78°  to  +  10° 

30-96 

5'4 

Rg. 

" 

0-189 
O'2O2 

9) 

99 

£ 

Rg- 
Kp. 

"          (red) 

0-I70 

5  '3 

Rg. 

Sulphur 

0-188 

31*98 

6'o 

D.P. 

„          rhombic 

0-163 

M 

5-2 

Kp. 

n                     >9 

O-I7I 

n 

5  "5 

Bn. 

J9                                99 

0-178 

57 

Rg- 

6  Potassium 

0-166 

-78°  to  +10° 

39!°4 

6'5 

Rg. 

Calcium 

0-I70 

39'9 

6-8 

Bn. 

Titanium 

0-1485 

o°  to  300° 

48 

7'i 

N.P. 

6  CompL  rend,  35.  278:  37.  130. 

7  //  Nuovo  Cimento  7.  321 ;  Abstract  in  Bull.  Soc.  Chitn.  for  1863.  171. 

8  Annalen,  Supplbd.  3.  i  and  289. 

9  When  no  temperature  is  given  the  determinations  were  made  somewhere 
between  the  limits  o°  and  100°:  the  numbers  may  in  these  cases  be  regarded  as 
approximately  the  mean  specific  heats  for  the  temperature-interval  40° — 60°. 

4—2 


ATOMS   AND   MOLECULES. 


[BOOK  i. 


Name 

Spec, 
heat 

Temp. 

Atomic 
weight 

Sp.  ht. 
x  at.  wt. 

Observer 

6  Chromium 

O'lO 

52-4 

5*2 

Kp. 

7  Manganese 

O*I22 

55 

67 

Iron 

0*112 

55  '9 

6*3 

Kp. 

J} 

0*114 

j? 

6-4 

Rg. 

5j 

O'HO 

« 

6-1 

DP. 

Nickel 

0-108 

58*6 

6-3 

Rg. 

Cobalt 

0-107 

59 

6'3 

Rg. 

Copper 

0-093 

63-4 

6-0 

Kp. 

„ 

0-095 

„ 

6-1 

Rg. 

55 

0-095 

6-1 

D.P. 

Zinc 

0-0932 

64-9 

6-1 

Kp. 

M 

0-0935 

„ 

6-1 

Bn. 

0-0955 

„ 

6*2 

Rg. 

5) 

0-093 

?> 

6-0 

D.P. 

8  Gallium 

0-079 

12°  tO  23° 

69 

5  '4 

Bt. 

Germanium 

0-077 

0°  tO  200° 

5-64 

N.P. 

Arsenic  —  amorphous 

0-076$ 

74'9 

B.W. 

„           crystalline 

0-083*): 

6"2 

B.W. 

J5                                    55 

0-0814 

w 

7*1 

Rg. 

55                                 55 

0-0822 

jj 

6*2 

N. 

9  Selenion  —  amorphous 

0-0746 

-27°  to  +8° 

78*8 

5'9 

Rg. 

„            crystalline 

0-0745 

-18°  to  +  7° 

B 

5'9 

Rg. 

55                                 5« 

0-0762 

9 

6*0 

Rg. 

55                                 55 

0-086  1 

B 

6*8 

N: 

55                                 55 

0-084$ 

}) 

6-7 

B.W. 

Bromine  —  solid 
10  Zirconium 

0-0843 
0-0666 

-78*  tO  -20° 

7975 
90*0 

67 
6-0 

Rg- 

M.D. 

11  Molybdenum 

0-0722 

95-8 

6-9 

Rg. 

Rhodium 

0-058 

104 

6*0 

Rg. 

Ruthenium 

0-06  1  1 

104-5 

6-4 

Bn. 

Palladium 

0-0593 

IO6'2 

6-3 

Rg. 

Silver 

0-056 

107-66 

6-0 

Kp. 

„ 

0-0559 

55 

6-0 

Bn. 

95 

0-057 

6-1 

Rg. 

Cadmium 

0-0542 

112 

6-0 

4. 

„ 

0-0548 

55 

6-1 

Bn. 

Indium 

0-0567 

0-057 

55 

6*5 

Rg. 

Bn. 

Tin 

0-0548 

II7-8 

6-5 

Kp. 

55 

0-0559 

55 

6*6 

Bn. 

>5 

0-0562 

6-6 

Rg. 

)5 

0-0514 

6-0 

D.P. 

Antimony 

0-0523 

I20'0 

6-2 

Kp. 

„ 

0-0495 

5  '9 

Bn. 

55 

0-0508 

6-0 

Rg. 

55 

0-0507 

6-0 

D.P. 

Tellurium 

0-0475 

125 

5'94 

Kp. 

Iodine 
Lanthanum 

0-0474 
0-0541 
0-0449 

126*53 
138*5 

5'94 
6-8 
6-2 

Rg. 
Rg. 

Hd. 

Cerium 

0-0448 

141 

6*3 

Hd, 

CHAP.  I.  §25]      SPECIFIC   HEATS  OF   ELEMENTS. 


53 


Name 

Spec, 
heat 

Temp. 

Atomic 
weight 

Sp.  ht. 

X  at.  WL 

Observer 

Didymium 

0-0456 

144 

6-5 

Hd. 

Tungsten 

0-0334 

183-6 

6-0 

Rg. 

Osmium 

0-03II 

193 

6-0 

Rg- 

Iridium 

0-0326 

194 

6-2 

Rg- 

Platinum 

0-0325 

195 

6-4 

Kp. 

» 

0-0324 

6'3 

Rg. 

0-0314 

» 

6'3 

D.P. 

12  Gold 

0-0324 

197 

6-3 

Rg. 

13  Mercury  —  solid 

0-0319 

-  78°  to  -  40° 

199-8 

6-4 

Rg. 

14  Thallium 

0-0335 

203-6 

6-8 

Rg. 

Lead 

0-0307 

206'4 

6-3 

Rg. 

'  yj 

0-0315 

» 

6-5 

Kp. 

0-0314 

» 

6-5 

Rg. 

Bismuth 

0-0305 

208 

6-3 

Kp. 

)) 

0*0308 

„ 

6'3 

Rg. 

Thorium 

0-0276 

232-4 

6-4 

Nn 

Uranium 

0-028 

240 

6-6 

Zn. 

Notes  to  preceding  Table. 

I  The  number  for  beryllium  is  that  calculated  by  Humpidge   from  a   series 
of  determinations  at  temperatures  varying  from  100°  to  450°  made  with  a  specimen 
of  beryllium  containing  99*2  per  cent,  of  the  metal:  for  fuller  discussion  of  specific 
heat  of  beryllium  see  par.  28,  pp.  62,  63. 

2-3-4  Spec,  heats  of  boron,  carbon,  and  silicon  are  discussed  on  pp.  63 — 65, 
par.  29. 

5  The  higher  temperature  (+  10°)  is  not  given  in  Regnault's  paper,  but  judging 
from  the  context  it  appears  to  be  approximately  correct. 

6  This  number  for  chromium  is  probably  too  low ;  see  Kopp,  Annalen,  Supplbd. 
3.  77  (note). 

7  The  specimen  of  manganese  employed  contained  a  little  silicon. 

8  Spec,  heat  of  molten  gallium  between  109°  and  119°= "0802.     (Berthelot, 
Bull.  Soc.  Ckim.  31.  229.) 

9  Spec,  heat  of  amorphous  selenion  determined  at  high  temperatures  is  ab- 
normal, because  of  the  large  quantity  of  heat  absorbed  before  fusion. 

10  Spec,  heat  of  zirconium  calculated  by  Mixter  and  Dana  from  determinations 
made  with  a  sample  containing  known  quantities  of  aluminium. 

II  The  specimen  of  molybdenum  employed  contained  carbon. 

12  Spec,  heat  of  gold  is  nearly  constant  from  o°  to  600° ;  at  900°  sp.  ht.  =  '0345  ; 
and  at  1000°=  "0352.     [Violle,  Compt.  rend.  89.  702.] 

13  Spec,  heat  of  liquid  mercury  at  55°=  '033  (Regnault). 

14  The  specimen  of  thallium  employed  contained  a  little  oxide. 

The  numbers  marked   with  J  are  probably  too   large;  see  Weber's  papers 
referred  to  in  next  page. 


54  ATOMS  AND  MOLECULES.  [BOOK  I. 

The  names  of  the  various  observers  are  abbreviated  in  the  table : — 

{Ann.  Chitn.  Phys.  [2]  73.  5  : 
[3]  1.  129:  9.  322:  26. 
261  :  38.  129:  46.  257: 
63.  5 :  and  67.  427. 

KP.        ,,     ,,     KOPP,  „         „         ,,         „         Annalen     126.      362 :     and 

Supplbd.  3.  i  and  289. 

N.         „     „    NEUMANN,      ,,        „        „        „        Fogg.  Ann.  126.  123. 

BN.        ,,     ,,     BUNSEN,          „        „        ,,         ,,        Pogg-  Ann.  141.  i. 

WB.       „     „     WEBER,  „        „        „         „        Pogg.  Ann.  154.  367  [trans- 

lation in  Phil.  Mag.  (4) 
49.  161  and  276.] 

D.  P.     „     „     Du LONG  and  PETIT,  „        „        Ann.  Chitn.  Phys.  10.  395. 

BT.       ,,     ,,     BERTHELOT,    „        ,,        „        „        Compt.  rend.  86.  786. 

HD.       ,,     ,,     HILLEBRAND,  „         ,,         „         Pogg.   Ann.  163.    71  [trans- 

lation in  Phil.   Mag.  (5) 
3.  109]. 

B.  W.  „     „    BETTENDORF  and  WULLNER      „        Pogg.  Ann.  133.  293. 

M.  D.   „     „     MIXTER  and  DANA,  „         „        Annalen,  169.  388. 

NN.       „     ,,     NILSON,  „         „         „         ,,         Ber.  15.  2519. 

HE.       „     „     HUMPIDGE      „        „        „        „         Proc.  R. S.  35.  137:  38.  1 88: 

39.  i. 

MT.      ,,     „    MALLET,         ,,        ,,        ,,        ,,        Chem.  News,  46.  178. 

ZN.       „     „     ZIMMERMANN  „        „        „        Ber.  15.  849. 

N.  P.    „    „    NILSON  and  PETTERSSON  „        Zeit.  f.  Physlkal.  Chetnie.  1. 

27. 
26        The  preceding  table  contains  the  names  of  5 1  elements, 

the  specific  heats  of  which  have  been  directly  determined. 
For  eleven  of  the  remaining  elements  values  have  been 

obtained  which  are  regarded  by  some  chemists  as  representing 

the  specific  heats  of  these  elements :   the  method  employed  is 

based  on  the  assumption  that  the  molecular  heat1  of  a  solid 

compound   is  equal  to  the  sum  of  the  atomic  heats  of  its 

constituent    elements.       (See    Kopp,    Annalen,    Supplh.    3. 

321 — 339.)     Thus  Kopp  found  the  mean  molecular  heat1  of 

metallic  sulphides  of  the  form  RS  to  be  equal  to    12:  the 

atomic  heat  of  sulphur  is  57;  but  12-57  =  6-3;  therefore 

6'3  is  regarded  as  the  value  of  the  atomic  heat  of  any  one  of 

the  metals  R.     The  mean  value  of  the  atomic  heats  of  these 

metals  found  by  direct  experiment  is  6'4. 

1  By  molecular  heat  is  to  be  understood  the  product  obtained  by  multiplying 
the  specific  heat  of  a  compound  into  the  mass  expressed  by  the  generally  accepted 
formula  of  that  compound;  the  expressions  formula-weight  and  reacting  weight 
will  be  employed  to  signify  this  mass  of  any  compound. 


CHAP.  I.  §26]  ATOMIC  HEATS  INDIRECTLY  DETERMINED.        55 

Kopp  has  applied  this  indirect  method  to  calculate  the 
atomic  heats  of  various  elements  with  which  direct  experi- 
ments could  not  be  made1. 
Chlorine:  — 
Molecular  heats  of  metallic  haloid  salts  :  — 

RC1  =12-8     RBr=i3'9     RI=i3'4 
RCl2=i8'5  .....................  RI2=i9'4. 

Now  as  (i)  the  atomic  heat  of  each  of  the  metals  R  is 
about  6-4  ;  (2)  the  atomic  heat  of  solid  bromine  and  that  of 
iodine  is  about  6'6;  (3)  the  chlorides,  bromides,  and  iodides 
examined  are  chemically  analogous;  and  (4)  the  molecular 
heats  of  the  analogous  salts  are  nearly  the  same  ;  Kopp  con- 
cludes that  the  atomic  heat  of  solid  chlorine  is  about  6-4. 

RC1  (i2-8)-R  (6-4)  =  6-4  :  RC12  (i8'5)-R  (6-4)  =  12-1,   and  ^  =  6-05. 

A  further  argument  in  favour  of  this  conclusion  is  afforded 
by  these  data:  — 

Molecular  heat  of  KC1O3  =  24'8 


hence  the  atomic  heats  of  arsenic  and  chlorine  are  probably 
nearly  the  same  ;  but  the  atomic  heat  of  arsenic  is  6'i  ;  there- 
fore the  atomic  heat  of  solid  chlorine  is  probably  about  6'i. 
Fhwrine  :  — 

Molecular  heat  of  CaF2=  16*4 
atomic  heat  of  Ca=  6'8, 

16-4-6-8 
hence  atomic  heat  of  fluorine  =  -  =4'o. 

Nitrogen  :  — 
Molecular  heats  of  various  more  or  less  analogous  compounds: 


RAsO3=25'3  RSiO3=2o'5 

RPO3=22'i  RNO3  =  23'o. 

Hence,  it  is  argued,  the  atomic  heat  of  solid  nitrogen  is 
probably  rather  less  than  that  of  chlorine  or  arsenic  (about  6), 
somewhat  greater  than  that  of  carbon  or  silicon  (about  5'2), 
and  nearly  equal  to  that  of  phosphorus  (about  5  '8);  therefore 
the  value  of  the  atomic  heat  of  solid  nitrogen  probably  lies 
between  5-5  and  5  '8. 

1  For  detailed  data  see  Kopp,  Annalen,  Supplb.  3.  329. 


56  ATOMS  AND  MOLECULES.  [BOOK  I. 

Oxygen :  the  molecular  heats  of  metallic  oxides  are,  as  a 
rule,  rather  less  than  those  of  corresponding  haloid  salts  ; 
therefore,  it  is  said,  the  atomic  heat  of  solid  oxygen  is  pro- 
bably less  than  6 ;  thus, 

RO  =iri RC1  =i2'8   RBr=i3'9   RI  =I3'4, 

RO2=i37 RCl2=i8'6 RI2=i9'4. 

Further  data  for  finding  the  value  sought  for  are  these  : — 

Molecular  heats R2O3  =  2/-2  ;  KAsO3=25'3  :  KC1O4  =  26'3; 

KMnO4=28'3. 

The  values  deduced  for  the  atomic  heat  of  solid  oxygen 
are  as  follows  : — 

from  RO  ...4*6,  from  KAsO3...4'2 

„    RO2...37,    „      KC1O4...3'5  [assuming  Cl  =  6] 
„  R203...4'8,    „    KMn04...3'8, 

hence  the  mean  value  is  4-1. 

Hydrogen :  the  principal  data  are  these : — 
(i)  Molecular  heat  of  ice  (H2O)  =  9  :  molecular  heat  of  Cu2O  =  15*6. 
Hence,  it  is  argued,  the  atomic  heat  of  solid  hydrogen  is 

probably  less  than  that  of  copper  by  the  amount  — =  3'3 : 

but  atomic  heat  of  copper  =  6*4 ;  therefore  the  atomic  heat  of 
solid  hydrogen  =  3-1. 

fbut  atomic  heat1  of  N  is  about  5'6) 

(n)  Molecular  heat  of  NH4C1  =  20:  \      ,  .    ,       .    .  _.  ?    \, 

[and  atomic  heat1  of  Cl       „        6'4j  ' 

o 

Now  20  —  12  =  8,  and  -  =  2  ;  therefore  the  atomic  heat  of 

4 
hydrogen  is  about  2. 

(iii)  Molecular  heat  of  NH4NO3  =  3 

„  oxides  R2O3  =  27-2 

Hence  36*4  -  27*2  =  9-2,  and  —  =  2*3. 

4 

The  mean  of  these  three  results  is  2-4,  a  number  which 
may  perhaps  be  provisionally  accepted  as  the  atomic  heat  of 
solid  hydrogen  :  the  method  of  calculation  however  involves 
many  assumptions  and  the  use  of  numbers  themselves  ob- 
tained by  indirect  means.  From  experiments  with  palladium 

1  Indirectly  determined,  see  p.  55. 


CHAP.  I.  §26]  ATOMIC  HEATS  INDIRECTLY  DETERMINED.        57 

charged  with  hydrogen,  Beketoff  deduced  the  number  5  '9  as 
representing  the  atomic  heat  of  solid  hydrogen  '. 

The  molecular  heats  of  the  oxides,  chlorides,  carbonates, 
nitrates,  and  sulphates,  of  calcium,  barium,  and  strontium  are 
nearly  the  same  as  the  molecular  heats  of  the  corresponding 
salts  of  metals  the  atomic  heats  of  which  have  been  directly 
determined  and  found  to  be  represented  by  the  mean  number 
6*4  ;  hence  the  atomic  heats  of  calcium,  barium,  and  strontium 
are  probably  represented  by  a  number  approximately  equal 
to  6-4. 

The  agreement  noticed  between  the  values  of  the  molecular 
heats  of  the  chloride  and  carbonate  of  rubidium,  of  the  oxides 
and  chlorides  of  chromium  and  titanium,  and  of  the  oxides  of 
vanadium  and  zirconium,  and  the  molecular  heats  of  corre- 
sponding salts  of  other  metals  which  themselves  exhibit  the 
mean  atomic  heat  6*4,  shews  that  the  atomic  heat  of  rubidium, 
that  of  titanium,  of  zirconium,  of  chromium,  and  of  vanadium, 
is  probably2  about  6-4.  (See  notes  6  and  10  to  table  of  speci- 
fic heats  of  elements,  p.  53.) 

The  following  numbers  representing  the  molecular  heats 
of  salts  of  some  of  the  rarer  elements  are  given  by  Nilson; 
(Ber.  13.  1459  et  se4-}- 

'{feat  C         Temperature.      "£»!» 

Scandium  salts  (80  =  44-03)    Sc2O3  °'I53  o°  —  100°         2O'8i 

Sc.23SO4  0-1639  »  62-42 

Erbium  salts  (E,r=\66)          Er2O3  0-065  »  247 

Er23SO4  0-104  „  64-5 

Yttrium  salts  (¥  =  89-5)          Y2O3  0-1026  „  23-3 

Y23S04  0-1319  „  6r6 

Ytterbium  sails  (Yb=i73)      Yb2O3  0-0646  „  25-5 

Yb23S04  0-104  „  '          65-8 


Gallium  oxide     Ga^j  0-1062  „  19-5 

Indium  oxide       In2O3  0-0807  „  22*2 

If  we  assume  that  the  atomic  heat  of  oxygen  is  4-1  (see 
p.  56),  and  regard  only  the  oxides  in  the  above  table,  then 

1  See  abstract  of  BeketofFs  paper  (original  is  in  Russian)  in  Ber.  12.  687. 

s  For  a  full  collection  of  specific  heat  data  see  F.  W.  Clarke's  Constants  of 
Nature,  part  n:  or,  Landolt  and  Bernstein's  Physikalisch-chemische  Tabcllen.  In 
connexion  with  this  subject  of  molecular  heats  see  also  Kopp,  Ber.  19.  Si  i. 


58  ATOMS  AND   MOLECULES.  [BOOK  I. 

the  following  values  are  found  for  the  atomic  heats  of  the 
metals  in  these  oxides  : — 

Sc=4'2  Er  =  6-i  Y=5'5  Yb  =  6'6 :  Ga=3'6  In  =  5'o. 
If  a  similar  process  is  applied  to  the  sulphates  (atomic  heat 
of  S  =  6),  then  the  atomic  heats  of  the  metals  are  all  repre- 
sented by  negative  numbers;  hence  either  (i)  the  value  of 
the  atomic  heat  of  oxygen  in  compounds  is  not  constant,  or 
(2)  that  of  sulphur  varies,  or  (3)  that  of  the  metals  Sc,  Er,  Y, 
Yb,  Ga,  In,  is  negative  in  their  sulphates,  and,  for  some  of 
these  metals,  is  abnormal  in  their  oxides. 

The  last  hypothesis  can  scarcely  be  adopted.  Indeed  if 
the  atomic  heats  of  gallium  and  indium  as  determined  by 
direct  experiment  are  placed  beside  the  numbers  obtained  by 
calculation  from  the  molecular  heats  of  the  oxides  (assuming 
O  =  4'i)  we  have  this  result : 

Directly  Calculated  from 

determined.  oxides. 

Atomic  heat  of  Gallium  5*4  3 '6 

„  Indium  6*5  5'o 

We  can  scarcely  hesitate  which  numbers  to  prefer. 

It  seems  then  that  the  value  to  be  assigned  to  the  atomic 
heat  of  oxygen  in  oxides1  (and  probably  also  the  value  of  the 
atomic  heat  of  sulphur  in  sulphates)  is  not  a  constant  number, 
but  varies  according  to  the  metal  with  which  the  oxygen  is 
combined2:  but  if  this  is  so,  much  doubt  must  necessarily  be 
thrown  on  the  accuracy  of  the  conclusions  regarding  the 
atomic  heats  of  chlorine,  nitrogen,  and  other  elements,  deduced 
from  the  molecular  heats  of  compounds  of  these  elements. 
It  appears  then  that  the  Garnier-Cannizzaro  generalisation 
(see  ante,  p.  51)  cannot  always  be  applied3. 

1  Such  phrases  as  'atomic  heat  of  oxygen  in  oxides,'  'atomic  heat  of  sulphur 
in  sulphates'  are  perhaps  rather  misleading;  they  seem  to  assume  that  an 
elementary  atom  has  different  capacities  for  heat  according  to  the  nature  (and 
number)  of  other  atoms  with  which  it  is  combined,  and  that  measurements  of 
these  various  capacities  are  obtainable;  this  assumption  is  not,  I  think,  fully 
justified  by  facts. 

8  See  Kopp,  Ber.  19.  813;  also  post,  chapter  in.  par.  in. 

3  Measurements  of  the  ratio  of  specific  heat  at  constant  volume  to  that  at 
constant  pressure  for  various  gases  composed  of  diatomic  molecules  have  shewn 
that  the  value  of  this  ratio  is  considerably  smaller  in  some  cases  than  in  others ; 


CHAP.  I.  §  26]  ATOMIC  HEATS  INDIRECTLY  DETERMINED.        59 

Although  a  knowledge  of  the  molecular  heats  (so-called) 
of  solid  compounds  may  give  considerable  help  towards  fixing 
the  formulae  of  these  compounds,  and  so,  indirectly,  deciding 
what  multiple  of  the  combining  number  of  an  element  is 
to  be  adopted  as  the  atomic  weight  of  that  element,  yet,  it 
appears  to  me,  that  so  far  as  concerns  the  direct  determination 
of  atomic  weights,  only  those  values  for  specific  heats  which 
have  been  obtained  by  experiments  on  the  solid  elements 
themselves  are  of  much  value. 

It  is  certain  that  in  some  cases  erroneous  conclusions 
regarding  the  value  of  an  atomic  weight  may  be  deduced 
from  measurements  of  the  specific  heats  of  solid  compounds. 
Thus  it  was  for  some  time  doubtful  whether  the  value  120 
or  240  should  be  assigned  to  the  atomic  weight  of  uranium. 
In  1878  Donath  found  the  specific  heat  of  uranoso-uranic 
oxide  to  be  -0798  (Ber.  12.  742);  assuming  the  specific  heat 

of  solid  oxygen  to   be  0*25  (i.e.  ^J ,  the    specific    heat   of 

uranium  was  calculated  to  be  -0497;  now  '0497  x  120=5*96; 
therefore  it  was  concluded  by  Donath  that  the  atomic  weight 
of  uranium  is  120.  But  in  1880 — I  pure  uranium  was  pre- 
pared by  Zimmermann  (for  details  see  Ber.  14.  440  and  779 : 
15.  849),  and  the  specific  heat  of  this  metal  was  found  by  him 
to  be  -028;  but  -028  x  120  =  3-3:  hence,  to  bring  the  atomic 
heat  of  uranium  into  agreement  with  that  of  the  majority  of 
the  elements  it  is  necessary  to  assign  to  the  atomic  weight 
of  this  metal  the  value  240. 
27  If  the  table  of  maximum  atomic  weights  (p.  48)  is  com- 

hence  a  complete  theory  of  specific  heat,  even  when  applied  to  gases,  must 
take  account  not  only  of  the  number  but  also  of  the  nature  of  the  atoms  in  a 
molecule  (compare  Ostwald,  Lehrbuch  der  allgemeinen  Chetnie,  1.  230).  When 
the  'molecular  heat'  of  a  compound  is  smaller  than  the  calculated  value  it  may 
be  that  the  molecule  of  the  compound  is  built  up  of  groups  of  atoms  each  of 
which  group  counts  as  a  single  atom.  If  the  atoms  forming  a  molecule  are 
symmetrically  arranged  (i.e.  if  the  distance  between  one  pair  of  atoms  is  much 
the  same  as  that  between  any  other  pair)  then  the  total  kinetic  energy  of  the 
molecules  is  very  probably  proportional  to  the  number  of  atoms ;  but  if  some  of 
the  atoms  are  arranged  in  groups  or  systems,  the  total  kinetic  energy  will  be 
proportional  to  the  number  of  systems,  and  not  to  the  number  of  atoms  (see 
'Aggregation,  States  of  in  the  new  Ed.  of  Watts's  Dictionary  of  Chemistry). 


60  ATOMS   AND   MOLECULES.  [BOOK  I. 

pared  with  that  which  gives  the  specific  heats  of  elements 
(pp.  51 — 53),  it  will  be  found  that — omitting  the  three  ele- 
ments which  are  placed  in  brackets  in  the  former  table — of 
the  43  elements  (omitting  those  in  brackets)  whose  atomic 
weights  have  been  determined  by  the  application  of  Avoga- 
dro's  law,  34  have  also  had  values  assigned  to  their  specific 
heats  by  direct  experiments.  Comparing  the  products  ob- 
tained by  multiplying  the  atomic  weight  into  the  specific  heat 
in  each  of  these  34  cases,  it  is  found  that  5  of  these  products 
fall  below  5 '8  (varying  from  57  to  5'2),  and  that  29  vary  from 
6'8  to  6,  giving  a  mean  value  of  6*4,  round  which  number  most 
of  the  values  are  grouped.  The  conclusion  to  be  drawn  is 
that  the  atomic  heat  of  the  29  elements  in  question  is  repre- 
sented by  the  number  6'4.  There  are  three  elements  in 
brackets  in  the  table  on  p.  48,  viz.  iron,  copper,  and  gallium  : 
if  the  maximum  atomic  weight  of  each,  as  deduced  by  Avo- 
gadro's  law,  is  multiplied  into  the  specific  heat  of  the  element 
the  product  is  found  to  be  about  12,  but  if  the  true  atomic 
weights  are  assumed  to  be  half  as  large  as  the  numbers  in  the 
table,  then  the  atomic  heat  of  each  of  these  elements  is  repre- 
sented by  the  mean  number  6'4-  Now  there  are  no  valid 
reasons  against  adopting  half  the  maximum  values  obtained 
by  Avogadro's  law  as  the  true  values  of  the  atomic  weights 
of  the  three  elements  in  question,  indeed  there  are  strong 
chemical  reasons  in  favour  of  this  course. 

Hence  we  have  a  very  considerable  mass  of  facts  in  favour 
of  the  generalisation  : — 

T/te  atomic  heat  of  all  solid  elements  is  nearly  a  con- 
stant, the  mean  value  of  which  is  6'4> 

If  this  be  granted,  we  deduce  the  statement  for  finding  an 
approximate  value  for  the  atomic  weight  of  an  element : — 

Atomic  weight  is  approximately  equal  to j —  ; 

provided  always  it  is  remembered  that  the  specific  heat  is 
assumed  to  be  determined  with  the  element  in  the  solid  form, 
and  for  a  considerable  range  of  temperature  throughout  which 
the  value  remains  nearly  constant. 

This  method  for  determining  the  atomic  weights  of  ele- 


CHAP.  I.  §27]  ATOMIC   HEATS.  6 1 

merits  has  been  applied  in  about  14  cases,  besides*  those 
cases  where  the  method  of  specific  gravities  has  also  been 
employed  ;  the  numbers  obtained  are  usually  regarded  as  the 
true  atomic  weights  of  the  elements  in  question. 

It  is  evident  that  in  determinations  of  the  specific  heats  of 
solid  elements  we  have  a  most  valuable  means  for  deciding 
which  multiple  of  the  combining  number  of  an  element  is 
to  be  accepted  as  most  probably  expressing  the  value  of 
the  atomic  weight  of  that  element.  When  the  element 
cannot  be  obtained,  or  cannot  be  obtained  in  sufficient  quan- 
tity, in  the  solid  form,  then  measurements  of  the  specific 
heats  of  a  series  of  its  solid  compounds  will  afford  more  or 
less  valuable  guidance  in  attempts  to  find  the  atomic  weight 
of  the  element  in  question. 

The  following  statements  fairly  sum  up  the  results  of 
atomic  heat  determinations. 

I.  Solid  elements,  forty-five  in  number,  whose  specific  Jieats 
have  been  directly  determined,  and  zvhose  atomic  heats  are  all 
nearly  equal  to  6^4. 

Li  Na  Mg  Al  P  S  K  Ca  Ti  Mn  Fe  Co  Ni  Cu  Zn  As 
Se  Br  Zr  Mo  Rh  Ru  Pd  Ag  Cd  In  Sn  Sb  Te  I  La 
Ce  Di  W  Os  Ir  Pt  Au  Hg  Tl  Pb  Bi  Th  U (Cr) 

II.  Solid  elements,  six  in  number,  wlwse  specific  heats  Jtave 
been  directly  determined,  and  whose  atomic  heats  appear  to  be 
about  5*5. 

Ga  [?  inaccurately  determined]     Be     B     C     Si     Ge. 

III.  Solid  elements,  five  in  number,   whose  specific  heats 
have  been  indirectly  determined,  and  whose  atomic  heats  are 
probably  nearly  equal  to  6'4. 

V     Rb     Sr     Cs     Ba. 

IV.  Gaseous  elements ;  atomic  heats  very  doubtful,  appa- 
rently variable. 

H     (F)    N     O    Cl. 

Of  the  elements  whose  atomic  heats  are  decidedly  less 
than  6-4,  all,  except  gallium  beryllium  and  germanium,  are 
non-metallic  and  have  atomic  weights  smaller  than  33:  indeed 
if  the  elements  are  arranged  in  order  of  increasing  atomic 
weight,  it  is  found  that,  with  the  exception  of  lithium,  all 
having  an  atomic  weight  less  than  23  have  also  an  atomic 


62  ATOMS   AND   MOLECULES.  [BOOK  I. 

heat  less  than  6,  and  that  these  elements,  except  beryllium, 
are  non-metallic. 

28        The  data  concerning  the  specific  heats  of  beryllium,  boron, 
carbon,  and  silicon,  must  be  examined  in  some  detail. 

Beryllium.  R.  E.  Reynolds  (Phil.  Mag.  (5)  3.  38)  deter- 
mined the  specific  heat  of  this  metal  at  100°  to  be  '642 :  the 
metal  used  was  however  impure. 

Nilson  and  Pettersson  (Ber.  11.351)  determined  the  specific 
heat  of  a  mixture  of  metallic  beryllium  with  known  quantities 
of  beryllium  oxide,  ferric  oxide,  and  silica  ;  they  also  deter- 
mined the  specific  heat  of  pure  beryllium  oxide,  and,  the 
specific  heats  of  ferric  oxide  and  silica  being  known,  they 
calculated  the  specific  heat  of  the  metal  beryllium  to  be  '4079, 
for  the  temperature  interval  o° — 100°. 

The  same  chemists  (Ber.  13.  1456:  see  also  Chem.  News, 
42.  297)  made  a  second  series  of  determinations  with  a  sample 
of  the  metal  containing  only  about  5  per  cent,  of  beryllium 
and  ferric  oxides.  The  following  table  gives  their  more 
important  results : — 

Specific  heat  of  Beryllium.     (NlLSON  and  PETTERSSON.) 


Temperature  interval. 

Specific  heat. 

Sp.hLx  13-65. 

o°—  46°  -5 

0'3973 

5  '4 

0°  —  100° 

0-4246 

5-8 

o°  —  214° 

0*475 

6-4 

o°—  300° 

0-5055 

6-9. 

Hence  these  chemists  concluded  that  the  atomic  weight 
of  beryllium  ought  to  be  taken  as  I3'65,  and  not  9-1,  the  value 
usually  assigned  to  this  constant 

The  results  tabulated  above  shew  that  the  value  of  the 
specific  heat  of  beryllium  for  the  interval  o° — 300°  is 

27  per  cent,  greater  than  the  value  for  the  interval  o° — 50° ;  is 
7  „  „  „  o° — 200° ;  and  is 

19  „  „  „  o°— 100°. 

Using  the  data  of  Nilson  and  Pettersson,  L.  Meyer  (Ber. 
13.  1780)  calculated  the  values  of  the  specific  heat  of  beryllium 
at  various  temperatures,  with  the  following  results  :— 


CHAP.  I.  §§28-29]      ATOMIC   HEAT   OF   BERYLLIUM.  63 

True  specific  heat  of  Beryllium  at  various  temperatures,  (MEYER.) 

7  =  true  specific  heat  at  temperature  /. 
Ay  =  increase  in  value  of  y  per  i°C. 


t. 

y- 

Ay. 

^=9-1 

^•=13-65 

20°'2 
73°'2 

0-3973 
0-4481'" 

O'OOIOI 

0-00085 

3-62 

4-08 

5'43 
6-12 

157° 

0-5193'" 

0*00063 

473 

7-10 

256°-8 

0-5819 

5-29 

8-94. 

Hence,  Meyer  concluded  that  the  specific  heat  of  beryllium 
increases  rapidly  as  temperature  increases,  but  that  the  rate 
of  this  increase  diminishes ;  and  that  the  specific  heat  pro- 
bably attains  a  constant  value,  equal  to  about  O"6,  at  300°  or  so1. 

Humpidge2,  working  with  a  specimen  of  beryllium  con- 
taining 99-2  per  cent,  metal  and  7  per  cent,  beryllium  oxide, 
obtained  the  following  numbers  : — 

Specific  heat  of  Beryllium.  (HUMPIDGE.) 

Temp.  Specific  heat. 

100°  '4702 

200°  -540 

400°  '6172 

500°  '6206. 

The  value  approximates  to  a  constant  (=  about  '62)  some- 
where between  400°  and  500°. 

Boron,  Carbon,  and  Silicon.  Very  varying  values  have 
been  obtained  for  the  specific  heats  of  these  three  ele- 
ments. The  following  table  summarises  the  principal  data 
previous  to  the  publication  of  Weber's  papers  [see  Phil.  Mag. 
(4)  49.  161  &  276]. 

Specific  heats  of  Boron,  Carbon,  Silicon.    (Weber's  numbers  not  included.) 
(Temperature  may  be  taken  as  about  35° — 55°.) 

Boron — amorphous 
„         crystalline 


Sp.  ht. 

Sp.  ht.Xat.  wt, 

Observer. 

0-254 

2-8 

Kp. 

1864 

0-230 

2-6 

» 

„ 

0-252 

2-8 

M.D. 

1873 

0*262 

2-9 

Rg. 

1869 

0'225 

2-5 

Rg. 

1869 

0-257 

2-8 

» 

» 

0-235 

2-6 

„ 

„ 

„        graphitic 

1  For  a  discussion  of  the  value  to  be  assigned  to  the  atomic  weight  of  beryllium 
see  chapter  in.  par.  1 1 1. 

2  Proc.  R.  S.3B.  137:  38.  1 88  :  and  specially  39.  I, 


SP.  ht. 

Sp.  ht.  X  at.  wt. 

Observer. 

0-143 

17 

B.W. 

1868 

0-147 

r8 

Rg- 

1841 

0-165 

2"O 

Kp. 

1864 

0-186 

2'2 

B.W. 

1868 

0-197 

2'4 

Rg. 

1841 

0-174 

2'I 

Kp. 

1864 

0-188 

2'3 

B.W. 

1868 

O'2OI 

2'4 

Rg- 

1866 

0-138 

3'9 

Kp. 

1864 

0-166 

4-6 

Rg. 

1861 

0*165 

4-6 

Kp. 

1864 

0'I7I 

4-8 

M.D. 

1873 

0-173 

4'8 

Rg. 

1861. 

64  ATOMS   AND   MOLECULES.  [BOOK  I. 

1  Carbon — diamond 

j>  » 

„          gas-carbon 

>i      .         » 
i>  » 

„          graphite 

»  »> 

»  >» 

Silicon — fused 

ii  » 

„          crystalline 


Weber  (loc.  at.}  found  that  the  specific  heats  of  carbon, 
boron,  and  silicon,  increase  rapidly  as  the  temperature  is 
raised,  but  that  at  high  temperatures  the  rate  of  the  increase 
becomes  much  smaller.  The  following  table  gives  a  synopsis 
of  Weber's  results : — 

Specific  heats  of  Boron,  Carbon,  and  Silicon.  (WEBER.) 

Temp.  Spec.  heat.        Spec.  ht.  x  at.  wt. 

Boron — crystallised  —40°  0-1915  2-11 

»                >»  +77°  0-2737  3-01 

»;  177°  0-3378  372 

»                 ii  233°  0-3663  4-03. 

These  numbers  shew  that  the  specific  heat  of  boron  in- 
creases with  increase  of  temperature,  and  that  the  value  of 
this  increase,  for  a  given  interval,  is  considerably  less  at  high 
than  at  low  temperatures.  The  variations  in  the  rate  of 
this  increase  are  almost  identical  with  the  variations  noticed 
in  the  case  of  carbon  ;  hence  at  temperatures  above  233° 
this  identity  will  probably  remain.  Calculated  on  this  as- 
sumption, the  specific  heat  of  boron  at  about  1000°  is  0*50. 

It  must  however  be  observed  that  Weber  did  not  prove 
the  purity  of  the  specimen  of  crystalline  boron  with  which  he 
worked.  The  crystals  were  prepared  by  reducing  boric  oxide 

1  Dewar  (Phil.  Mag.  [4]  44.  461)  found  for  the  specific  heat  of  gas-carbon 
between  20°  and  1040°  the  number  0-32,  for  diamond  the  number  o'366;  and, 
between  20°  and  a  temperature  estimated  to  be  2000°,  for  'carbon'  the  number 
0-42. 


CHAP.  I.  §  29]        ATOMIC   HEAT   OF   CARBON.  65 

by  aluminium  ;  according  to  Hampe  (Annalen,  183.  75)  the 
substance  thus  obtained  is  a  definite  boride  of  aluminium, 
A112B. 

Specific  heats  of  Boron,  Carbon,  and  Silicon.    (WEBER)  continued. 

Temp.  Spec.  heat.          Sp.  ht.  x  at.  wt. 

Carbon — diamond  -50°  0-0635  0-76 

„  „  +10°  0-1128  1-35 

„  „  85°  0-1765  2'12 

250°  0-3026  3-63 

„  „  606°  0-4408  5-29 

985°  0-4589  5-50 

„  graphite  -  50°  0-1138  1*37 

„  „  +10°  0-1604  1-93 

„  61°  0-1990  2-39 

„  „  201°  0-2966  3-56 

„  250°  0-325  3-88 

„  »  641°  0-4454  5'35 

„  978°  0-467  5-60 

Porous  wood  carbon  o° — 23°  0-1653  1*95 

o°— 99°  0-1935  2-07 

o°— 223°  0-2385  2-84. 

These  numbers  shew  that  the  specific  heat  of  carbon 
increases  from  —  50°  upwards,  the  value  found  at  600°  being 
about  seven  times  as  great  as  that  found  at  —  50° ;  but  that 
the  rate  of  this  increase  is  very  small  at  high  temperatures ; 
from  a  red  heat  upwards  the  rate  is  about  one-seventeenth 
of  that  from  o°  to  100°. 

The  specific  heats  of  diamond  and  graphite  differ  at  tem- 
peratures below  about  600°,  but  from  this  point  upwards  they 
are  practically  identical ;  the  numbers  given  for  porous  wood 
carbon  are  almost  the  same  as  those  for  graphite  for  the  same 
temperature-intervals ;  hence  it  may  be  said  that  at  high 
temperatures  (above  600°)  the  various  modifications  of  carbon 
have  probably  all  the  same  specific  heat. 

Table  continued. 

p.  Temp.  Spec.  heat.          Sp.  ht. x at.  wt. 

Silicon — crystallised  -40°  0*136  3-81 

»  »  +57°    '  Q'i833  5'i3 

„  „  128°  0-196  5-50 

„  „  184°  0-20 1  I  5-63 

»  „  232°  0-2029  5-68 

M.C.  5 


66  ATOMS   AND  'MOLECULES.  [HOOK  I. 

The   specific  heat  of  silicon  attains  an  almost  constant 
value  at  about  200°. 

30  It  is  evident  that  the  specific  heat  of  an  elementary 
body  is  not  a  constant  number,  but  varies  with  the  tem- 
perature, and  that  the  relation  between  the  variation  of 
specific  heat  and  that  of  temperature  differs  for  each  element. 
The  following  formulae  calculated  from  experimentally  deter- 
mined numbers,  express  the  relation  in  question  for  some  of 
the  elements : — 

1  Carbon— diamond  sp.  ht.  =  0-4408  +  0-0000405  /,  where  /  varies  from 

6oo°— 800° 

„                „  „  =  0-4408  +  0-000056 1 1  „  8oo°— 1000° 

„          graphite  „  =  0*4454  +  0*0000472  /  „  600° — 800° 

„                „  „  =0-4454  + 0-0000840  /  „  8oo°— 1000° 

2Copper  „  =  0-0910  +  0*000023 1  „  o° — 250° 

2Zinc  „  =0-0865  +  0*000044 1  „  „ 

2  Lead  „  =0-0286  +  0-000019 1  „  „ 
3Platinum  „  =  0*03 1 7  +  o'ooooo6  /  „  o° — 1200° 

The  specific  heat  of  any  substance  also  varies  with  varia- 
tions in  the  physical  state  of  that  substance,  thus  : — 


Sp.  heat. 

Bromine — solid     ...         ...  0-0843 

„          liquid  ...         ...  OTIIO 

Soft  copper  0-0948 

Hard  copper          ...         ...  0*0934 

Iron  sulphide  as  strahlite  0-1332 


Sp.  heat. 

Iron  sulphide  as  pyrites  ...  0-1279 

Chlorine — solid     ...         ...  o'i8o 

„  4  gaseous         ...  0*093 

Mercury — solid     ...         ...  0*032 

„  4gaseous          ...  0-015 


The  specific  heats  of  the  elementary  bodies  have  gener- 
ally been  determined  at  temperatures  situated  at  very  varying 
intervals  from  the  melting  points  of  these  elements  ;  the 
physical  aggregation  of  the  specimens  examined  has  also 
varied  much ;  hence  the  values  found  for  the  specific  heats 
of  the  elements  cannot  be  regarded  as  strictly  comparable. 

There  appears  to  be  a  certain  interval  of  temperature 
within  which  the  value  of  the  specific  heat  of  a  solid  element 
becomes  nearly  constant,  and  for  this  interval  only  can  the 
element  be  said  approximately  to  obey  the  law  of  Dulong 

1  Weber  (loc.  fit.). 

2  Bede,  Mem.  Couronn.  de  FAcad.  Brux.  27.  3  (1855). 

3  Violle,  Compt.  rend.  85.  543. 

4  Calculated  for  constant  volume. 


CHAP.  I.  §§30-31]  ATOMIC   HEATS.  67 

and  Petit,  as  stated  on  p.  60.  This  temperature-interval 
varies  for  each  element,  especially  for  the  nonmetallic  ele- 
ments with  small  atomic  weights ;  for  many  elements  it  may 
be  roughly  taken  as  from  o°  to  100° ;  but  for  several  it  is  only 
attained  at  high  temperatures. 

Kopp  (loc.  tit.}  has  supposed  that  the  atoms  of  certain 
elements — more  especially  of  boron,  carbon,  and  silicon — are 
built  up  of  simpler  parts,  have  themselves  a  grained  structure, 
and  that  at  high  temperatures  the  atoms  of  these  elements 
are  composed  of  a  smaller  number  of  those  little  parts  than  at 
lower  temperatures.  Heat  added  at  low  temperatures  is 
supposed,  on  this  hypothesis,  to  be  used  in  separating  the 
atomic  groups.  With  regard  to  Kopp's  hypothesis  it  may  be 
observed,  that  the  facts  of  spectroscopy  seem  to  point  to  the 
existence  of  a  more  complex  structure  in  the  nonmetallic  than 
in  the  metallic  molecules ;  that  allotropy  occurs  distinctly 
only  among  the  non-metals ;  that  the  molecules  of  the  five 
metallic  elements  whose  vapour-densities  have  been  deter- 
mined are  monatomic ;  that  the  atomic  heat  of  tellurium,  a 
metal-like  non-metal  belonging  to  the  oxygen  group,  is  6-o,  of 
the  less  metal-like  selenion  about  5'8,  of  the  decidedly  non- 
metallic  sulphur  about  5'5,  and  of  the  typical  non-metal  oxygen 
probably  not  more  than  4;  and  finally  that  the  molecular 
structures  of  oxygen,  sulphur,  and  selenion,  vapours  are  more 
complex  than  that  of  tellurium  vapour.  Now  as  carbon, 
boron,  and  silicon  are  distinctly  non-metallic  elements,  these 
facts  lend  support  to  the  view  that  a  part  of  the  heat  added 
to  carbon,  boron,  or  silicon,  at  low  temperatures  is  spent  in 
separating  complex  molecular  groups  into  their  constituent 
parts,  rather  than  in  separating  the  hypothetically  complex 
atoms  of  these  elements  into  smaller  atoms. 

31  A  consideration  of  the  data  summarised  in  the  preceding 
paragraphs  shews,  I  think,  that  the  application  of  Avogadro's 
law  is  of  more  value  to  the  chemist  as  a  means  of  determining 
the  atomic  weights  of  elements  than  the  law  of  Dulong  and 
Petit.  From  a  general  consideration  of  the  molecular  theory 
of  matter  it  is  also  apparent  that  a  deduction  which  does  not 
necessitate  an  exact  hypothesis  as  to  the  internal  structure  of 

5—2 


68  ATOMS   AND   MOLECULES.  [BOOK  I. 

molecules  is  more  trustworthy  and  more  appropriate,  in  the 
present  state  of  knowledge,  than  another  which  does  necessi- 
tate some  such  hypothesis. 

The  molecular  explanation  of  the  gaseous  laws  expressing 
relations  between  volume,  pressure,  and  temperature,  and  of 
Avogadro's  law,  may  be  considered  as  fairly  complete  ;  but  in 
order  to  give  a  molecular  explanation  of  the  law  of  specific 
heats  more  knowledge  of  the  internal  structure  of  molecules 
than  we  now  possess  is  necessary1.  For  the  specific  heat  of  a 
substance  depends  on  the  rate  at  which  the  whole  energy  of 
the  molecule  increases  with  increase  of  temperature  :  but  this 
energy  is  made  up  of  two  parts,  (i)  the  energy  of  agitation, 
that  is,  the  energy  the  molecule  would  possess  if  it  moved  as  a 
whole  with  the  motion  of  its  centre  of  mass,  or  in  other  words 
without  rotation  ;  and  (2)  the  energy  of  rotation,  that  is,  the 
energy  the  molecule  would  possess  if  its  centre  of  mass  were 
reduced  to  rest,  in  other  words  the  energy  due  to  the  motion 
of  the  parts  relatively  to  the  centre  of  mass  of  the  molecule2. 
If  it  is  assumed  that  the  energy  due  to  the  rotational  motions 
of  the  parts  of  the  molecule  tends  towards  a  value  having  a 
constant  ratio  to  the  energy  of  agitation  of  the  molecule, 
then  a  simple  expression  is  found  for  the  whole  energy  ;  but 
this  expression  contains  a  factor  which  varies  in  different 
gases,  and  the  value  of  which  has  been  determined  only  in  a 
few  cases3.  And  moreover  it  is  probable  that  when  the  energy 
due  to  the  rotational  motions  of  the  parts  of  a  molecule 
becomes  greater  than  a  certain  quantity,  the  molecule  separates 
into  parts ;  hence  when  heat  is  imparted  to  a  mass  of  mole- 
cules work  is  probably  in  many  cases  done  in  destroying 
some  of  the  molecules  as  such4.  Hence  the  molecular  expla- 
nation of  specific  heat  is  not  at  present  in  so  advanced  a  state 
as  that  of  the  relations  between  the  volumes,  pressures,  and 
temperatures,  of  gases5.  If  this  be  true  concerning  gases,  still 

1  Clerk  Maxwell,  C.  S.  Journal  [2]  13.  507. 

3  Clerk  Maxwell,  lot.  cit.  p.  502. 

8  See  Clerk  Maxwell's  Heat,  pp.  317—319  (6th  ed.). 

4  See  Hicks,  Phil.  Mag.  (5).  4.  80,  and  174.     'On  some  effects  of  Dissocia- 
tion on  the  Physical  Properties  of  Gases. ' 

5  See  in  connexion  with  this  subject  Strecker,  Wied.  Ann.  13.  20;  and  Bolt;;- 


CHAP.  I.  §§  31-32]  ISOMORPHISM.  69 

more  is  it  true  concerning  solid  bodies.  Our  knowledge  of 
the  molecular  phenomena  of  solids  is  very  small ;  but  the  law 
of  Dulong  and  Petit  is  applicable  to  solid  elements  only. 
Finally,  when  heat  is  added  to  a  solid  only  a  portion  of  it  is 
used  in  raising  the  temperature;  another  part  is  spent  in 
increasing  the  volume  of  the  solid,  and  a  third  part  is  em- 
ployed in  doing  work  against  the  external  pressure  on  the 
solid. 

32  The  so-called  '  law  of  isomorphism '  affords  a  basis  on 
which  is  founded  another  method  for  determining  the  atomic 
weights  of  elementary  bodies. 

The  views  of  Abbe  Haiiy  were  dominant  in  crystallo- 
graphy in  the  early  days  of  this  century ;  he  admitted 
a  close  connexion  between  crystalline  form  and  chemical 
composition,  but  he  thought  that  each  chemically  dis- 
tinct body  must  be  characterised  by  a  definite  and  peculiar 
form. 

In  1816  Gay-Lussac  noticed  that  the  growth  of  crystals 
of  potash  alum  was  not  affected  by  placing  them  in  a  solution 
of  ammonia  alum. 

Various  observations  of  this  kind  were  made  from  time  to 
time1  until  1819,  when  E.  Mitscherlich  propounded  the  law  of 
isomorphism,  which,  modified  and  developed,  was  stated  by 
him  in  1821  in  the  following  terms:  "  Equal  numbers  of  atoms 
similarly  combined  exhibit  tJie  same  crystalline  form  ;  identity 
of  crystalline  form  is  independent  of  t/te  chemical  nature  of 
the  atoms,  and  is  conditioned  only  by  the  number  and  configura- 
tion of  the  atoms." 

Since  this  date  various  observers  have  advanced  the  know- 
ledge of  the  relations  between  crystalline  form  and  chemical 
composition2.  The  more  important  generalisations  are  as 
follows. 

mann,  Jo.  13.  544:  and  18.  309:  also  art.  Aggregation,  States  of,  in  the  new 
edition  of  Watts' s  Dictionary. 

1  For  a  full  historical  account  of  the  development  of  the  conception  of  Iso- 
morphism, with  copious  references,  see  the  article  'Isomorphie'  in  the  Neues 
Handivortcrbuch  der  Chemie,  Bd.  ill.  p.  844  el  seq. 

*  See  especially  ffandworterbuch,  loc.  at.  and  Kopp's  Lchrbuch  der  physikal- 
ischcti  und  thcorctischcn  Chcinic  (2nd  Ed.),  Bd.  II.  pp.  136—155. 


70  ATOMS   AND   MOLECULES.  [BOOK  I. 

Similar  chemical  constitution1  is  not  necessarily  accom- 
panied by  identical  crystalline  form  ; 
e.g.  PbCrO4  monoclinic,  and  PbMoO4  quadratic ; 

AgCl  and  AgBr  regular,  and  Agl  hexagonal ; 

KNO3   and    (NH4)NO3    rhombic    but    not    identical,    CsNO3    and 
RbNO3  hexagonal. 

Unlike  chemical  constitution  may  be  accompanied  by 
similar  or  identical  crystalline  form  :  thus  Marignac2  shewed 
that  the  following  salts  crystallise  in  identical  forms ; — 

K2TiF6.  H2O,  K2NbOF5.  H2O,  K2WO2F4.  H2O,  are  isomorphous ; 
andCuTiF6.4H2O,  CuNbOF5.4H2O,  CuWO2F4. 4 H2O,  are  isomorphous. 
Klein3  has  shewn  that  the  complex  compounds 
9WO3.  B2O3.  24H2O  and  I2WO3.  SiO2.33H2O,  and 
9\VO3 .  B2O3 .  Na2O  .  23H2O,  are  isomorphous. 

Klein  has  modified  the  statement  of  the  law  of  isomor- 
phism thus : 

"  Isomorphous  bodies  have  either  a  similar  chemical  constitution  or 
exhibit  only  slight  differences  in  percentage  composition ;  there  is  always  a 
group  of  elements  which  is  either  common  to  all  the  isomorphous  bodies, 
or  exhibits  identical  chemical  functions  in  these  bodies,  and  which 
constitutes  by  far  the  greater  part  of  each  of  the  isomorphous  bodies." 

It  would  appear  that  all  the  constituents  of  a  compound 
exert  an  influence  on  the  form  of  that  substance.  Isomorphism 
may  not  be  exhibited  in  comparatively  simple  analogous 
compounds  of  two  elements,  but  may  appear  in  more  complex 
compounds  of  the  same  elements  ;  e.g.  many  of  the  simpler 
compounds  of  cadmium  are  not  isomorphous  with  the  analo- 
gous compounds  of  the  metals  of  the  magnesium  group  (Mg, 
Mn,  Fe,  Co,  Ni,  Zn,  Cu,  Ca),  but  comparatively  complex 
cadmium  salts — such  as  CdSO4.  K2SO4.6H2O — are  generally 
isomorphous  with  the  corresponding  compounds  of  the  mag- 
nesian  metals.  Again,  many  simple  salts  of  sodium  and 
potassium  are  not  isomorphous  although  their  composition  is 
similar,  but  the  alums  are  isomorphous. 

1  This  phrase  must  not  be  interpreted  too  strictly.     Closely  allied  compounds 
the  formula;  of  which  contain  the  same  number  of  elementary  atoms,  or  groups  of 
atoms,  may  be  said,  for  the  purposes  of  the  present  argument,  to  exhibit  a  '  similar 
chemical  constitution.' 

2  Ann.  Chim.  Phys.  60.  257.  3  Compt.  rend.  95.  781. 


CIIAIM.§32]  ISOMORPHISM.  71 

One  may  suppose  that  the  presence  of  a  large  number  of 
isomorphous  atoms  exerts  a  dominating  influence  over  a 
smaller  number  of  non-isomorphous  atoms. 

The  constituents  of  isomorphous  compounds  are  not  them- 
selves always  isomorphous.  Thus,  the  sulphates  of  nickel, 
magnesium,  and  zinc,  crystallise  in  rhombic  forms,  but  the 
oxides  of  the  same  elements  are  not  isomorphous. 

In  other  cases  the  constituents  of  isomorphous  bodies  are 
themselves  isomorphous  ;  e.g.  the  compound  3Ag2S  .  Sb2S3  has 
the  same  crystalline  form  as  the  compound  3Ag8S .  As2S3, 
Sb2S3  and  As2S3  are  isomorphous  in  rhombic  forms,  and 
arsenic  and  antimony  form  almost  identical  rhombic  crystals. 
Hence  we  must  distinguish  strict  isomorphism  as  applied  to 
bodies  which,  with  similar  composition,  exhibit  the  same  or 
nearly  the  same  crystalline  form  ;  and  isomorphism  as  more 
loosely  applied  to  bodies  which,  although  not  themselves 
crystallising  in  the  same  form,  nevertheless  combine  with 
other  bodies  to  produce  strictly  isomorphous  compounds  into 
which  they  enter  as  corresponding  groups1. 

A  certain  latitude  is  generally  allowed  in  the  application  of 
the  term  '  isomorphous  crystals.'  This  latitude  has  gradually 
been  more  and  more  advanced  until  it  has  become  difficult  to 
give  an  exact  meaning  to  the  expression.  Absolute  identity 
of  the  angles  of  two  bodies  occurs  only  when  the  bodies 
crystallise  in  the  regular  system.  Chemically  analogous  com- 
pounds sometimes  crystallise  in  forms  closely  resembling  one 
another,  yet  belonging  to  different  systems;  e.g.  potassium 
dichromate  crystallises  in  monoclinic  forms,  where  a  :  b  :  c 
=  roii6  :  i  :  rSi45,  and  ammonium  dichromate  crystal- 
lises in  triclinic  form  the  relations  of  the  axes  of  which  are 
nearly  the  same  as  those  of  the  monoclinic  crystals,  viz.  a\b:c 
=  1-0271  :  i  :  17665.  Salts  with  identical  crystalline  form 
sometimes  exhibit  optical  differences2.  Are  all  such  salts  to 
be  called  truly  isomorphous  ?  Kopp3  proposes  that  only  those 
salts  any  one  of  which  is  capable  of  growing  in  unmodified 

1  Lehrbuch  der  physikalischen  und  theoretischeii  Chemie,  2.  139. 

2  See  Baker,  C.  S.  Journal  Trans,  for  1879.  760. 

3  Ber.  12.  goo  et  seq. 


72  ATOMS   AND   MOLECULES.  [BOOK  I. 

form  when  immersed  in  a  solution  of  any  other  should   be 
regarded  as  strictly  isomorphous1. 

33  As  we  know  the  crystalline  form  of  comparatively  few 
elements2,  the  statement  that  such  or  such  elements  form 
an  isomorphous  group,  generally  means  only  that  the 
analogous  compounds  of  these  elements  are  for  the  most  part 
isomorphous. 

The  more  important  groups  of  isomorphous  elements,  as 
thus  understood,  are  as  follows 3 : — 

GROUP  I.     Fluorine,  Chlorine,  Bromine,  Iodine,  [Cyanogen];   in  all 
compounds  : 

partially  Manganese;  in  compounds  of  the  type  RMnO4. 

GROUP  II.     Sulphur,  Selenion;  in  all  compounds  and  as  elements  in 
monosymmetric  forms : 

partially  Tellurium;  in  compounds  of  the  type  RTe  : 

„          Chromium,  Manganese,  Tellurium;  in  salts  of  their  acids 

belonging  to  the  type  H2RO4 : 
„         Arsenic,  Antimony;  in  compounds  of  the  type  RS2. 

GROUP  III.     Arsenic,  Antimony,  Bismuth,  Tellurium;  as  elements, 
and  the  three  first-named  in  all  corresponding  compounds : 

partially  Phosphorus  and  Vanadium;  in  salts  of  their  acids : 

„         Nitrogen    with   phosphorus,    arsenic,    and    antimony ;    in 
organic  bases. 

GROUP  IV.     Lithium,  Sodium,  Potassium,  Rubidium,  Cizsium,  \Arn- 
moniutti\  ;  in  most  compounds  : 

partially  Thallium;  in  some  compounds  : 

,,         Silver,  in  some  compounds  (especially  with  sodium}. 

GROUP  V.     Calcium,  Strontium,  Barium,  Lead;  Magnesium,  Zinc, 
Manganese,  Iron;  e.g.  in  carbonates : 

partially  Nickel,  Cobalt,  Copper;  with  iron  in  some  compounds,  e.g. 
sulphates : 

1  Lehmann,   Zeitschr.  f.  Physikal.   Chemie,   1.   15,   49,   has   recorded  a  few 
cases  of  non-isomorphous  compounds  crystallising  together,  e.g.  CuCl2.2H2O  and 
NH4C1.      Many  precautions  must  be  taken  in  the  practical  application   of  this 
criterion  of  isomorphism  (s.  '  Isomorphie '  in  Ladenburg's  Handuwrterbuch  der 
Chemie,  5.  385). 

2  See,  for  the  crystalline  forms  of  elements  in  the  free  state,  Watts's  Dictionary 
[ist  Ed.],  vol.  in.  p.  429. 

3  From  article  '  Isomorphie '  in  Neues  Handivorterbuch,  loc.  cit.     For  a  much 
fuller  account  of  the  isomorphism  of  elements,  see  Ladenburg's  Hand-war terbuch 
dcr  Chenric,  5.  394. 


CHAT.  I.  §33]  ISOMORPHOUS  ELEMENTS.  73 

partially  Lanthanum,  Cerium,  Didymium,    Yttrium,  Erbium;   with 

calcium,  in  compounds  of  type  RO: 
„          Copper,  Mercury;  with  lead,  in  oxy-compounds  : 
„         Beryllium,  Cadmium,  Indium;  with  zinc,  in  some  com- 
pounds: 
„          Thallium;  with  lead,  in  some  compounds. 

GROUP  VI.  Aluminium,  Chromium,  Manganese,  Iron;  in  the  sesqui- 
oxides  [R2O3]  and  salts  derived  therefrom  : 

partially  Cerium,  Uranium;  in  their  sesquioxides. 

GROUP  VII.     Copper,  Silver;  in  compounds  of  the  type  R2O  : 
partially  Gold;  with  silver, 

GROUP  VIII.     Ruthenium,  Rhodium,  Palladium,  Iridiiim,  Platinum, 
Osmium;  in  most  compounds  : 
partially  Iron,  Nickel,  Gold: 
„          Tin  \?  Tellurium~\. 

GROUP  IX.     Carbon,  Silicon,  Titanium,  Zirconium,  Tin,  Thorium; 
partially  in  compounds  of  the  type  RO2,  and  salts  derived  from  the 
type  H2RO3:  carbon  with  silicon  in  many  correspond- 
ing so-called  organic  compounds. 
„         Iron;  with  titanium. 
GROUP  X.    Niobium,  Tantalum;  in  all  their  compounds. 

GROUP  XI.     Molybdenum,  Tungsten;  in  all  their  compounds: 
partially  Chromium;  in  salts  of  acids  of  the  type  H2RO4. 

The  terms  dimorphous,  trimorphous,  polymorphous  were 
used  by  Mitscherlich.  Many  examples  of  the  phenomena  to 
which  these  names  are  applied  are  now  known :  thus  calcium 
carbonate  crystallises  in  hexagonal  forms  as  calcspar,  and  in 
rhombic  forms  as  arragonite;  titanium  oxide  assumes  two 
distinct  quadratic  forms,  one  being  known  as  rutile  the  other  as 
anatasc,  and  it  also  crystallises  as  brookite  in  rhombic  prisms ; 
arsenious  oxide  crystallises  in  octahedral,  antimonious  oxide 
in  rhombic,  forms,  but  if  amorphous  arsenious  oxide  is 
heated  in  a  sealed  tube  so  that  one  part  of  the  tube  is  at  400° 
and  the  rest  below  this  temperature,  the  oxide  deposited  in 
the  middle  part  of  the  tube  is  found  to  be  isomorphous  with 
rhombic  antimonious  oxide;  the  latter  oxide  is  also  known  in 
octahedral  forms,  so  that  the  isodimorpJiism  of  these  two 
oxides  is  complete1. 

1  s.  Lehmann,  Zeitsch r.  f.  physikal.  Chetttie,  1.  15. 


74  ATOMS   AND   MOLECULES.  [BOOK  I. 

34  If  it  is  assumed  that,  as  a  general  rule,  those  masses  of 
two  substances  which  are  crystallographically  equivalent 
have  similar  chemical  constitutions1;  and  if  we  suppose 
that  the  atomic  weights  are  known  of  the  elements  which 
compose  one  of  two  compounds  exhibiting  identical  or  nearly 
identical  crystalline  form,  it  is  evident  in  what  way  deter- 
minations of  crystalline  form  may  aid  in  fixing  atomic 
weights. 

To  take  an  example : — from  determinations  of  the  specific 
gravities  of  gaseous  compounds  and  analyses  of  these  com- 
pounds, the  value  52*4  is  assigned  to  the  atomic  weight  of 
chromium ;  this  number  is  verified  by  measurements  of  the 
specific  heat  of  the  same  metal.  The  green  oxide  of  chromium 
exhibits  the  same  crystalline  form  as  ferric  oxide,  hence 
these  oxides  should  probably  be  represented  by  similar  for- 
mulae. On  comparing  the  compositions  of  crystallographically 
equivalent  quantities  of  the  two  oxides,  it  is  found  that  one  is 
composed  of  52^4  x  2  parts  by  weight  of  chromium  and 
1 5 '96  x  3  parts  of  oxygen,  and  the  other  of  the  same  mass  of 
oxygen  combined  with  SS'9  x  2  parts  by  weight  of  iron.  Now 
the  atomic  weight  of  chromium  has  been  determined  to  be 
52-4,  and  the  atomic  weight  of  oxygen  is  known  to  be  I5'96; 
hence  the  simplest  formula  that  can  be  given  to  the  green 
oxide  of  chromium  is  Cr2O3;  and  hence  the  probable  formula 
of  ferric  oxide  is  Fe2Os.  But  if  the  latter  formula  is  correct  it 
follows  that  2  atoms  of  chromium  are  replaced  from  one 
reacting  weight  of  the  oxide  Cr2O3  by  2  atoms  of  iron.  If  this 
conclusion  is  granted,  the  atomic  weight  of  iron  is  55-9.  As 
the  specific  heat  of  iron  multiplied  into  55*9  gives  the  product 
6'4,  5  5 '9  is  almost  certainly  the  true  atomic  weight  of  iron. 
Again,  the  formulae  of  potassium  perchlorate  and  permanga- 
nate were  at  one  time  written  KO .  C1O7  and  KO .  Mn2O7. 
Berzelius  proposed  the  formulae  KO.C1O7  and  KO.MnO7, 
which  on  the  system  of  notation  now  adopted  become  KC1O4 
and  KMnO4  respectively;  these  formulae  represent  crystallo- 
graphically equivalent  quantities  of  the  two  salts;  if  it  is 
assumed  that  Cl  (35'37)  represents  the  weight  of  the  atom  of 
1  See  note  i.  p.  70. 


CHAP.  I.  §34]         APPLICATION    OF   ISOMORPHISM.  75 

chlorine,  then  Mn  (55)  probably  represents  the  weight  of  the 
atom  of  manganese. 

Observations  of  crystalline  form  have  sometimes  led  the 
way  to  correct  determinations  of  atomic  weights,  or  to  changes 
in  the  received  values  of  such  weights.  Thus  H.  Rose1  gave 
the  name  of  hyponiobium  to  a  supposed  allotropic  form  of 
the  metal  niobium;  but  Marignac2  shewed  that  compounds 
of  the  hypothetical  metal  were  identical  in  crystalline  form 
with  certain  compounds  of  tin  and  titanium,  and  concluded 
that  Rose's  hyponiobium  was  itself  isomorphous  with  the 
atomic  groups  SnF  and  TiF,  and  was  therefore  probably  a 
compound.  Further  experiments  shewed  that  the  hypo- 
niobium  of  Rose  was  really  composed  of  niobium  and  oxygen 
in  the  proportions  expressed  by  the  formula  NbO  (Nb  =  94) ; 
now  if  it  was  admitted  that  the  groups  of  atoms  NbO,  SnF, 
and  TiF,  were  crystallographically  equivalent,  it  followed, 
from  the  analyses  of  the  various  compounds,  that  one  atom 
of  tin  or  titanium  (117*8  or  48  parts  by  weight  respectively) 
was  replaced  by  94  parts  by  weight  of  niobium,  and  that  this 
number  therefore  represented  the  weight  of  the  atom  of 
niobium8. 

Again,  the  isomorphism  of  the  double  compound  of  gal- 
lium and  ammonium  sulphates  with  ordinary  ammonia-alum 
shewed  that  the  former  salt  was  a  true  alum  ;  hence  the 
formula  X23SO4.  (NH4)2SO4.24H2O  was  applicable  to  the 
salt  in  question.  But  in  the  case  of  common  alum  X2  =  A12  = 
2.  x  27'O2;  and  in  the  case  of  gallium  alum  X2=  138  :  hence,  as 
two  atoms  of  aluminium  were  replaced  by  138  parts  by  weight 
of  gallium,  it  followed  that  the  atomic  weight  of  gallium  was 
J-|p  =  69.  This  number  was  confirmed  by  the  analysis  of 
gaseous  gallium  chloride. 

1  P°Sg'  Ann.  108.  273. 

8  Ann.  Chim.  Phys.  60.  257. 

3  Marignac's  conclusions  were  afterwards  confirmed  by  determinations,  by 
Deville  and  Troost,  of  the  specific  gravity  of  gaseous  chloride  and  oxychloride  of 
niobium:  see  Compt.  rend.  69.  1221. 

Roscoe's  researches  on  the  atomic  weight  of  vanadium  afford  a  very  in- 
structive example  of  the  employment  of  the  results  of  crystallographic  measure- 
ments in  fixing  atomic  weights.  Phil.  Trans,  for  1868,  I.  et  seq. 


76  ATOMS   AND   MOLECULES.  [BOOK  I. 

The  facts  of  which  an  outline  has  been  given  shew  that 
until  more  extended  and  precise  knowledge  of  the  connexions 
between  crystalline  form  and  chemical  constitution  is  ob- 
tained, that  method  for  determining  the  atomic  weights  of 
elements  which  is  founded  on  these  connexions  can  be  applied 
only  tentatively  and  in  a  limited  number  of  cases.  The 
method  may  however  now  be  of  considerable  service  in 
suggesting  lines  of  research  bearing  on  the  problems  con- 
nected with  atomic  weight  determinations. 

It  appears  probable  that  the  crystalline  form  of  a  sub- 
stance is  connected  at  once  with  the  internal  structure  of  the 
molecules  of  the  substance  and  with  the  configuration  of  the 
molecules  themselves.  No  attempt  has  been  made,  nor  can 
in  the  present  state  of  knowledge  hopefully  be  made  in  any 
but  the  broadest  manner,  to  apply  to  the  facts  of  crystallo- 
graphy the  theory  of  the  molecular  structure  of  matter. 
35  Many  attempts  have  been  made  to  determine  molecular 
weights  by  other  physical  methods  than  the  three  already 
described.  Of  these  attempts,  that  made  by  Raoult  has 
led  to  important  results1.  This  chemist  has  determined  the 
amount  of  lowering  of  the  freezing  point  of  water,  and  various 
other  solvents,  produced  by  dissolving  quantities  of  various 
compounds  proportional  to  the  formula-weights,  or  reacting 
weights,  of  these  compounds  ;  he  has  found  that  chemically 
similar  compounds  generally  produce  equal  lowerings  of  the 
freezing  points  of  water  and  some  other  solvents. 

Let  P  grams  of  a  compound  be  dissolved  in  100  grams  of 
water,  or  other  solvent,  and  let  the  observed  lowering  of  the 

freezing  point  be  C\  then  -p  =  coefficient  of  lowering  of  freezing 

point  for  the  compound  in  question.     If  M=  molecular  weight, 
or  better,  formula-weight,  of  a  specified  compound,  then  the 

product  -p  M  is  called  by  Raoult  the   molecular  lowering  of 

freezing  point.  M  -pis  constant  for  all  the  members  of  the  same 

class  of  compounds  ;  thus  Raoult  finds  the  following  values, 
water  being  the  solvent : — 

1  s.  especially  Ann.  Chim.  Phys.  [6]  8.  317. 


CHAP.  I.  §  35]     DETERMINATION    OF   ATOMIC   WEIGHTS.         77 


19  for  organic  compounds,  except  oxalic  acid  and  compound 

ammoniums  ; 
35  for  all  salts  of  monovalent  metals  with  monobasic  acids, 

e.g.  NaCl,    NaC2H8O2)    NaNO3  ; 

40  for  all  normal  salts  of  monovalent  metals  with  dibasic  acids, 
e.g.    (NH4)2S04,    K2C03)    K2CrO4; 

etc.  etc.  etc. 

When  benzene  was  the  solvent,  Raoult  found  the  values:  — 


49  for    all    organic   compounds    except   acids,  alcohols,  and 

phenols  ; 
25  for  the  lower  members  of  homologous  series  of  alcohols. 

Raoult  found  other  constant  values  when  other  solvents, 
e.g.  acetic  acid,  were  employed. 

If  the  value  of  M  -=  for  a  group  of  compounds  is  known,  it 

is  possible  to  find  the  formula-weight  of  a  member  of  the  group 
from  observations  of  the  coefficient  of  lowering  of  freezing 
point  of  that  compound.  Thus  to  take  the  case  of  ether. 

(i)    4'47  grams  of  ether  were  dissolved  in  100  grams 
of  water,  and  the  freezing  point  of  the  water  was  lowered  by 

—  -     '° 
4'47 

ganic  compounds  dissolved  in  water  is  19;  therefore  in  the 
present  case  M—  -^  =  82. 

(ii)    2721  grams  of  ether  dissolved  in   100  grams  of 
benzene  lowered  the  freezing  point  by  i°'826  ;  therefore  the 

coefficient  of  lowering  was  —  -  =  '671°.  Now  as  M  -p  =  49 
for  the  class  of  compounds  of  which  ether  is  a  member,  it 
follows  that  M=  -^-  =  73. 

(iii)     The  coefficient  of  lowering  of  freezing  point  of 
acetic  acid  for  ether  was  determined  to  be  '529°. 


i°'O5  ;  hence  -75=  —  -  =  '23°.     But  the  value  of  M  -~  for  or- 
r       ' 


78  ATOMS   AND   MOLECULES.  [BOOK  I. 

Experiments  had  shewn  that  M  p=  39  for  all  organic  and 
many  inorganic  compounds  ;  hence  in  the  present  case 


The  mean  of  the  three  results  gives  the  value  76-6  for  the 
formula-weight  of  ether  ;  the  correct  value  is  74. 

This  method  is  of  wide  application  for  determining  the 
reacting  (or  formula)  weights  of  compounds,  and  is  especially 
useful  as  it  is  applicable  to  bodies  which  cannot  be  gasified 
without  decomposition. 

36  I  have  endeavoured  to  shew  that  the  most  trustworthy 
method  for  determining  molecular  and  atomic  weights  is 
founded  on  Avogadro's  law,  which  is  itself  an  outcome  of 
the  application  of  dynamical  reasoning  to  a  physical  theory. 
Formerly  it  was  supposed  that  strictly  chemical  evidence 
must  be  of  paramount  importance  in  determining  these  quan- 
tities. Although  the  superior  importance  of  Avogadro's  law 
is  now  admitted,  this  law  can  only  be  applied  to  a  limited 
number  of  substances,  hence  we  are  frequently  obliged  to 
have  recourse  to  purely  chemical  evidence  in  support  of  this 
or  that  molecular  weight.  The  nature  of  such  chemical 
evidence,  and  the  modifications  in  the  physical  conception  of 
molecular  weight  to  which  it  leads,  must  now  be  shortly 
illustrated. 

In  1850  Brodie1  endeavoured  to  shew  that  there  is  no 
difference  of  kind  between  those  reactions  wherein  elementary 
bodies  are  produced,  or  react,  and  those  in  which  compound 
bodies  are  alone  concerned.  He  supposed  that  the  small 
particles  of  elementary  substances  set  free  during  reactions, 
or  taking  part  in  reactions,  are  composed  of  smaller  parts 
which  exhibit  certain  mutual  polar  relations.  Silver  chloride 
is  not  decomposed  by  oxygen,  but  it  readily  interacts 
with  potassium  oxide  with  production  of  silver  oxide  and 
potassium  chloride  ;  hydriodic  and  iodic  acids  decompose 
one  another  with  production  of  free  iodine  ;  silver  oxide 
decomposes  hydrogen  peroxide  to  form  silver,  water,  and  free 

1  Phil.  Trans,  for  1850,  759,  and  also  C.  S.  Journal,  4.  194. 


CHAP.  I.  §36]      DETERMINATION    OF   ATOMIC   WEIGHTS.         79 

oxygen,  half  of  the  oxygen  coming  from  the  silver  oxide  and 
half  from  the  peroxide  ;  iodine  decomposes  barium  peroxide 
with  production  of  barium  iodide  and  oxygen.  These  re- 
actions were  thus  written  by  Brodie  (translating  into  the  new 
notation): — 


(i)     AgAgClCl  +  KKO  =  AgAgO  +  KKClCl 

(+»nd 

(2) 


(3) 
(4) 

That  part  of  Brodie's  hypothesis  which  supposed  a  polar 
condition  of  atoms  in  molecules  was  not  generally  adopted 
by  other  chemists,  but  it  was  admitted  that  his  researches 
established  a  general  similarity  of  function  and  composition 
between  elementary  and  compound  molecules. 

In  the  same  year  Williamson1  distinguished  between  the 
atom  of  zinc  in  combination,  and  the  free  metal  zinc  (that  is 
to  say,  he  recognised  that  the  atom  of  an  element  is  not 
possessed  of  the  same  properties  as  the  molecule  of  that 
element)  :  he  said  it  is  not  quite  accurate  to  speak  of  '  zinc  ' 
as  existing  in  zinc  sulphate. 

Recognising  then  that  chemical  reactions  took  place  be- 
tween molecules,  chemists  defined  the  molecule  as  the  smallest 
part  of  a  substance  capable  of  taking  part  in  a  chemical 
change,  or  as  the  acting  chemical  unit.  Supposing  the  atomic 
weights  of  the  elements  forming  a  compound  to  be  known, 
the  best  method  of  determining  the  molecular  weight  of  the 
compound  appeared  to  be  to  find  that  formula  which  should 
express  the  atomic  composition  in  the  simplest  manner. 
Thus  ammonia  is  formed  by  the  combination  of  hydrogen 
and  nitrogen  in  the  proportion  of  3  parts  by  weight  of  the 
former  to  14  of  the  latter  ;  assuming  the  atomic  weights  of 
these  elements  to  be  I  and  14  respectively,  the  atomic  com- 
position of  ammonia  may  be  represented  by  the  formula  NH,. 
As  the  reactions  in  which  this  substance  takes  part  might 
all  be  represented  as  involving  17,  or  a  whole  multiple  of  17, 

1  C.  S.  Journal,  4.  355. 


80  ATOMS  AND   MOLECULES.  [BOOK  I. 

parts  by  weight  of  this  compound,  and  moreover  as  hydrogen 
could  be  removed  from  17  parts  by  weight  of  ammonia  in 
three  separate  and  equal  parts  by  chemical  reactions,  17  was 
taken  to  be  the  molecular  weight  of  ammonia. 

An  instructive  illustration  of  this  method  of  fixing  a 
minimum  molecular  weight  is  furnished  by  Williamson's 
famous  researches  on  ethers '.  The  formulae  generally  adopted 
for  common  alcohol  and  ether,  previous  to  Williamson's  work, 
were  C4HfiO2  and  C4H5O  respectively  (C  =  6 ;  O  =  8).  William- 
son allowed  ethylic  iodide  to  react  on  potassium  alcoholate, 
expecting  that  ethylated  alcohol  would  be  produced — thus 
C4H5KO2  +  C4H5I  should  give  C4H5(C4H5)O2  +  KI— but  the 
product  was  ordinary  ether.  If  the  generally  accepted  formula 
for  ether  were  doubled  the  reaction  would  be  explained,  and 
ether  would  be  regarded  as  an  oxide  of  ethyl  (C4H5)2O2. 
Again,  Williamson  found  that  when  sulphuric  acid  acts  on 
ethylic  alcohol,  and  methylic  alcohol  is  added  to  the  mixture, 
a  single  substance  having  the  properties  of  an  ether,  and  the 
formula  C3H4O  or  a  whole  multiple  of  this  formula,  distils 
over.  If  the  formula  of  ether  is  C4H5O,  then  that  of  methylic 
ether  is  C2H3O,  and  a  mixture  of  these  ought  to  be  obtained 
in  the  reaction  just  mentioned  ;  but  if  ether  is  (C4H5)2O2,  then 
the  single  ether  obtained  is  probably  methyl-ethyl  oxide2, 
i.e.  C4H5(C2HS)O2  (=2C3H4O).  Thus  was  shewn,  on  purely 
chemical  grounds,  the  necessity  of  doubling  the  generally 
accepted  molecular  formula  for  ether. 

No  purely  chemical  method  capable  of  general  application 
has  been  found  for  determining  molecular  weights  ;  each  com- 
pound must  be  considered  as  a  separate  problem.  The  more 
important  methods  may  however  be  roughly  classified. 

There  is  the  method  of  analogies,  which  is  well  illustrated 
by  the  example  of  ether  already  considered.  The  smallest 
amount  of  sulphuretted  hydrogen  which  takes  part  in  chemi- 
cal changes  is  represented  by  the  formula  H2S  (assuming 
S  =  32),  the  hydrogen  in  this  compound  is  replaceable  in  two 

1  See  C.  S.  Journal,  4.  106,  and  229. 

2  Translated  into   modern   notation,    these    formulae   become   (C2H5),O  and 
C2H5(CH3)0  respectively. 


CHAP.  I.  §36]  ATOMIC   WEIGHTS.  8 1 

parts — with  production  of  KHS  and  KKS — hence  the  mole- 
cular formula  is  not  less  than  H2S.  But  compounds  of  selenion 
and  tellurium  with  hydrogen,  analogous  in  general  properties 
to  sulphuretted  hydrogen,  are  known ;  from  the  marked 
similarity  between  these  two  elements  and  sulphur  it  is  very 
probable  that  the  molecular  formulae  of  the  two  compounds 
in  question  are  H2Se  and  H2Te  respectively:  as  these  formulae 
satisfy  the  analytical  numbers,  they  may  be  adopted.  The 
simplest  formula  that  can  be  given  to  acetic  acid — con- 
sistently with  the  values  H  =  i,  C  =  12,  and  O  =  16 — is  CH2O. 
But  if  this  acid  is  neutralised  by  soda  and  the  sodium  salt 
thus  produced  is  analysed,  it  is  found  that  this  salt  contains 
one  atom  of  sodium  (the  atomic  weight  of  sodium  is  assumed 
to  be  known,  =  23)  in  combination  with  three-fourths  of  the 
quantity  of  hydrogen  present  in  the  original  acid,  the  quan- 
tities of  carbon  and  oxygen  being  unchanged.  Hence,  it  is 
argued,  one-fourth  of  the  total  hydrogen  of  the  acid  has  been 
replaced  by  sodium ;  but  not  less  than  one  atom  of  hydrogen 
(or  another  element)  can  be  removed  from  a  molecule ;  hence, 
as  one  atom  of  hydrogen  out  of  four  atoms  has  been  replaced 
by  sodium,  it  follows  that  the  molecule  of  acetic  acid  contains 
at  least  four  atoms  of  hydrogen.  But,  in  order  to  express 
this  conclusion,  the  formula  of  the  acid  must  be  written 
C2H4O2;  and  therefore  the  minimum  molecular  weight  of 
acetic  acid  is  60.  This  conclusion  is  confirmed  by  the  pre- 
paration of  thiacetic  acid,  which  is  composed  of  16  parts  by 
weight  of  oxygen  (i.e.  one  atom)  less  than  enters  into  the 
composition  of  acetic  acid,  the  quantities  of  carbon  and 
hydrogen  remaining  the  same,  and  32  parts  by  weight  of 
sulphur.  Now  if  the  atomic  weight  of  sulphur  is  known  to 
be  32,  it  follows  that  the  minimum  molecular  weight  of  acetic 
acid  is  expressed  by  the  formula  C2H4O2,  and  that  of  thiacetic 
acid  by  the  formula  C2H4OS. 

The  formula  for  water  was  once  written  HO.  If  potas- 
sium is  thrown  on  to  water  hydrogen  is  evolved,  and  the 
solid  product  of  the  reaction  is  a  white  salt  whose  compo- 
sition may  be  expressed  by  the  formula  HO.KO(O  =  8). 
But  this  substance  is  undecomposed  by  heat,  and  it  exhibits 
none  of  the  reactions  which  a  compound  of  water  with  a 
M.  C.  6 


82  ATOMS   AND   MOLECULES.  [BOOK   I. 

metallic  oxide  might  be  expected  to  possess,  nevertheless  it 
is  composed  of  hydrogen,  oxygen,  and  potassium  ;  when  it  is 
fused  with  potassium,  hydrogen  is  evolved  and  potassium 
oxide  remains.  The  oxygen  of  this  compound  cannot  be 
removed  in  parts.  If  the  molecular  formula  of  water  is 
written  H2O(O=i6)  these  facts  are  explained;  the  white 
solid  then  becomes  KOH,  and  this  formula — as  the  minimum 
molecular  formula  of  the  compound — is  confirmed  by  the 
close  analogies  which  exist  between  the  properties  of  this 
body  and  those  of  alcohol,  the  molecular  formula  of  which 
has  been  determined  to  be  (C2H5)  OH.  If  steam  reacts  with 
chlorine  or  bromine  oxygen  is  evolved,  and  a  compound  of 
hydrogen  and  chlorine  (or  bromine)  is  produced,  the  simplest 
formula  for  which  is  HC1  (or  HBr);  no  compound  of  oxygen, 
hydrogen,  and  chlorine  (or  bromine)  is  formed  and  oxygen  at 
the  same  time  evolved.  Hence,  it  is  argued,  the  hydrogen  in 
the  molecule  of  water  is  divisible  in  chemical  changes  into 
two  parts,  but  the  oxygen  is  not  divisible,  and  hence,  the 
simplest  molecular  formula  for  water  is  H2O  ;  but  if  this  is  so, 
the  atomic  weight  of  oxygen  cannot  be  less  than  16. 

The  following  generalisation  is  quoted  from  Horstmann1. 

"  When  we  know  that  -  of  a  constituent  of  a  molecule  can  be  replaced 

ft 

by  another  constituent,  the  composition  of  the  molecule  remaining  in 
other  respects  unchanged,  it  follows  that  the  given  molecule  must  contain 
at  least  n  atoms  of  the  first-named  constituent,  inasmuch  as  parts  of  an 
atom  cannot  be  removed  from  a  molecule....  If  the  atomic  weight  of  the 
replacing  constituent  is  known  the  minimum  molecular  weight  of  the 
original  substance  can  be  found,  because  it  is  easy  to  calculate  from  the 
empirical  composition  of  the  substance  how  much  of  the  other  constituents 
must  be  present  in  combination  with  n  atoms  of  the  replacing  body." 

Assuming  the  atomic  weights  of  iron  and  oxygen  to  be 
(in  round  numbers)  56  and  16  respectively,  the  formula  Fe2O3 
is  deduced  from  analyses  of  ferric  oxide  as  representing  the 
smallest  quantity  of  this  compound  which  neutralises  one  or 
more  reacting  weights  of  various  acids,  forms  double  com- 
pounds with  other  oxides  &c.  the  reacting  weights  of  which 

1  Lehrbuch  der  physikalischen  und  theoretischen  Chemie.  Zweite  Abtheilung; 
Theoretische  Chemie  (eimchliesslich  der  Thermochemie)  von  Dr  A.  Horstmann 
(1885),  p.  86. 


CHAP.  I.  §  36]  ATOMIC   WEIGHTS.  83 

are  known,  interacts  with  chlorine  to  form  Fe8Cl6,  &c.  ;  hence 
this  formula  represents  the  minimum  molecular  weight  of 
ferric  oxide.  But  similar  reasoning  leads  to  As2O8  as  the 
minimum  molecular  formula  of  arsenious  oxide;  now  we 
know  that  the  gaseous  oxide  has  a  molecular  weight  ex- 
pressed by  the  formula  As4O6.  Hence  the  method  of  ana- 
logies does  not  always  lead  to  the  adoption  of  the  true 
molecular  weight  of  a  compound. 

It  should  be  noted  here  however  that  by  '  the  true  mole- 
cular weight'  is  meant  the  relative  weight  of  the  gaseous 
molecule  ;  but  the  chemical  methods  for  rinding  molecular 
weights  only  profess  to  determine  the  relative  weights  of  the 
chemically  reacting  units  of  bodies. 

Sometimes  the  method  of  analogies  becomes  very  indirect. 
Thus,  ferric  chloride  has  been  gasified  and  the  molecular  for- 
mula of  this  compound  is  known  to  be  Fe2Cl6  :  the  simplest 
formula  that  can  be  given  to  ferrous  chloride  is  Fed2;  is 
this,  or  a  multiple  of  this,  to  be  adopted  as  the  molecular 
formula  of  ferrous  chloride  ?  Ferric  chloride  is  produced  by 
the  action  of  chlorine  on  ferrous  chloride  ;  now  the  general 
action  of  chlorine  is  either  to  add  itself  on  to  other  molecules, 
or  to  decompose  molecules  and  then  substitute  itself  for  some 
one  or  more  of  the  atoms  formerly  constituting  these  mole- 
cules. If  ferrous  chloride  is  FeCl2,  the  action  of  chlorine  on  this 
molecule  is  represented  by  the  equation  2FeCl2  +  Cl2  =  Fe2Cl6  ; 
but  such  a  reaction  as  this  does  not  often  occur.  If  ferrous 
chloride  is  Fe2Cl4,  the  action  of  chlorine  is  represented  by 
the  equation  Fe2Q4  +  C12  =  Fe2Clfi,  and  this  reaction  is  ana- 
logous to  other  actions  of  chlorine  ;  hence  the  molecular  for- 
mula of  ferrous  chloride1  is  probably  not  smaller  than  Fe2Cl4. 

The  chemical  method  of  determining  minimum  molecular 
weights,  as  applied  to  acids  and  bases,  generally  resolves  itself 
into  determining  the  basicity  of  the  acid,  or  the  acidity  of  the 
base.  Thus,  the  results  of  analyses  of  sulphuric  acid  are 
satisfied  by  the  formula  H^S^O^  ;  the  fact  that  this  acid  is 


1  V.  Meyer  has  obtained  results  regarding  the  vapour  density  of  ferrous  chloride 
which  seem  to  him  to  point  to  the  conclusion  that,  like  stannous  chloride,  this 
compound  possesses  two  molecular  weights  expressed  respectively  by  the  formulae 
FeCl.2and  Fe2Cl4;  Ber.  14.  1455;  17.  1335. 

6—2 


84  ATOMS   AND   MOLECULES.  [BOOK   I. 

dibasic  leads  with  a  fair  degree  of  certainty  to  the  con- 
clusion that  x=\,  and  that  the  molecular  formula1  of  the 
compound  is  therefore  H2SO4.  The  simplest  formula  which 
can  be  given  to  citric  acid  consistently  with  analytical  results, 
and  with  the  atomic  weights  C  =  12,  O  =  16,  H  =  I,  is  C6H8O7; 
that  the  molecular  formula1  is  probably  not  greater  than  this 
is  shewn  by  the  tribasic  character  of  the  acid.  Reasons 
have  been  already  given  for  adopting  NH3  as  the  true  mole- 
cular formula  of  ammonia ;  analysis  shews  that  the  alkaloid 
quinine  cannot  have  a  smaller  molecular  weight  than  that 
represented  by  the  formula  C10H12NO  (C  =  12,  H  =  i,  N  =  14, 
O  =  1 6) ;  but  the  quantity  of  this  alkaloid  which  neutralises 
that  amount  of  hydrochloric  acid  which  is  neutralised  by 
NH3,  is  2C,0H12NO ;  therefore  the  molecular  formula1  of 
quinine  is  probably  not  less  than  C20H24N.,O2. 

This  method  may  also  be  applied  to  determine  the  formulse 
of  salts.  Thus  if  sulphuric  acid  has  the  molecular  formula1 
H2SO4,  the  molecule  of  sodium  sulphate  is  probably  repre- 
sented by  the  formula  Na2SO4,  because  the  atom  of  sodium 
being  very  probably  monovalent2,  the  amount  of  sodium 
'equivalent'  to  2H  is  represented  by  2Na.  So,  although  ortho- 
boric  acid  is  non-volatile,  its  ethyl  salt  has  been  vaporised  and 
found  to  have  the  formula  (C2H5)3BO3,  hence,  knowing  that 
ortho-boric  acid  is  tribasic,  we  deduce  for  it  the  probable 
molecular  formula1  H3BO3. 

The  so-called  'law  of  even  numbers'  enunciated  by  Ger- 
hardt  led  to  the  revision  of  many  molecular  formulae : 
Gerhardt  stated  that  the  sum  of  certain  elementary  atoms 
(hydrogen,  chlorine  and  its  analogues,  nitrogen  and  its  ana- 
logues) contained  in  any  molecule  is  always  an  even  number3. 
Thus,  analysis  leads  to  the  formula  C2H3O3  for  tartaric  acid, 
and  as  the  acid  is  dibasic  this  formula  is  apparently  mole- 
cular; but  the  hydrogen  atoms  must  be  expressed  by  an 
even  number  according  to  Gerhardt's  law,  therefore  the 

1  That  is,  the  formula  expressing  the  smallest  mass  of  the  body  capable  of 
taking  part  in  a  chemical  change. 

2  That  is,  capable  of  combining  directly  with  not  more  than  one  atom  of 
hydrogen,  chlorine,  bromine,  iodine,  or  fluorine,  to  form  a  compound  molecule. 
See  chap.  II.,  pars.  56,  57. 

3  See  Laurent,  Chemical  Method,  p.  46  et  seq. 


CHAP.  I.  §§  36—38]       ATOMIC   WEIGHTS.  85 

formula  was  doubled.  Similar  reasoning  applied  to  the 
formula  of  nitric  oxide  would  require  this  to  be  written  N2O2 ; 
but  we  know  that  the  moleculaj  formula  of  this  compound 
is  NO  ;  hence  Gerhardt's  'law'  must  be  applied  with  care1. 

37  The  chemical   methods  for  determining  reacting  weights 
and  atomic  weights  differ  in  two  main  particulars  from  the 
physical  method  for  determining  molecular  and  atomic  weights 
which  is  based  on  the  molecular  theory. 

The  chemical  methods  as  a  class  do  not  attempt  to 
distinguish  between  solids,  liquids,  and  gases ;  so  far  as 
the  application  of  these  methods  is  concerned  the  reacting 
weight  of  a  solid,  liquid,  or  gaseous,  substance  is  the  smallest 
mass  of  that  substance  which  takes  part  in  a  chemical  re- 
action :  the  physical  method  for  finding  molecular  weights  is 
strictly  applicable  only  to  gases  ;  but  the  terms  in  which  the 
physical  definition  of  molecule  is  stated  are  much  more 
precise  than  those  which  describe  the  chemical  conception 
of  reacting  weight. 

The  chemical  methods  sometimes  attempt  to  determine 
the  atomic  weights  of  the  elements  which  form  a  specified 
compound,  and  from  these  and  other  data  to  deduce  the  re- 
acting weight  of  the  compound ;  sometimes  the  reacting 
weight  of  the  compound  is  first  determined,  and  then  de- 
ductions are  drawn  regarding  the  atomic  weights  of  the 
constituent  elements.  The  physical  method,  on  the  other 
hand,  begins  by  defining  molecule,  and  then,  applying  this 
definition  to  chemical  reactions,  arrives  at  a  definition  of 
atom,  both  definitions  being  so  stated  as  to  indicate  the  data 
which  are  required  before  the  relative  weights  of  either  atoms 
or  molecules  can  be  determined. 

38  In  the  following  table  I  have  sought  to  summarise  many 
facts  concerning  the  atomic  weights  of  the  elements:  it  is  well 
that  the  student  should  have  placed  before  him  a  synopsis  of 
the  evidence  on  which  these  all-important  numbers  are  based. 

1  For  further  examples  of  the  application  of  chemical  methods  to  determina- 
tions of  molecular  and  atomic  weights  see  Watts's  Diet,  (ist  Ed.)  vol.  I.  pp.  45?— 8 
and  460—1  ;  also  Williamson  'On  the  Atomic  Theory,'  C.  S.  Journal,^.  328. 
See  also  Chapter  III.  of  this  Book,  The  Periodic  Law. 


86 


ATOMS   AND   MOLECULES. 
Atomic  Weights  of  the  Elements. 


[BOOK  T. 


I 

I 

II 

III 

IV 

Principal  compounds, 

Element 

vapour  densities  of 
which  have  been 

Specific  heat  : 
horu  determined 

Isomorphism  : 
compounds  compared 

determined 

[See  note  A,  p.  92. 

HYDROGEN 

HF,    HC1,    HBr,    HI, 
H2S,      H2Se,      H2Te, 
H3N,  H3P,  H4C,  &c. 

ndirectly  [from  sp.  heat  of  H2O, 
NH4C1,  NH4NO3] 
[atomic  heat  abnormal?] 



LITHIUM 

none 

directly 

Li    compounds    with    analogous 

compounds  of  alkali  metals 

BERYLLIUM 

BeBr2,  BeCl2 

directly  :   sp.    heat  varies    much 

a  few  Be  compounds  with  analo- 

with temperature 

gous  compounds  of  Cd  and  Zn 

BORON 

BF3,        BC13,        BBr3, 

directly:   sp.    heat  varies   much 



B(CH3)., 

with  temperature 

CARBON 

CH4,     CH3F,     CH3C1, 
CH3Br,  CH3I,  CHCI3, 
CO,CO2,COC12,COS, 

directlv  :    sp.  heat   varies   much 
with  temperature 

CN  compounds  with  those  of  F, 
Cl,  Br  and  I 

NITROGEN 

CS2,    CHN,    C2H6O, 
C4H,00,  &c. 
NH3,  NO,  NO2,  NOC1, 
N2O,  N2O4)  &c. 

indirectly:  very  undecided 
[from   sp.   ht.    of    various    com- 

NH4  compounds  with    those    of 
alkali  metals 

pounds] 

OXYGEN 

OH2,  ON,,  OC,  OC13P, 
02C,  02S,  03S,  040s, 

indirectly:  very  undecided 
[from    sp.   ht.   of   various  .com- 



&c. 

pounds] 

FLUORINE 
SODIUM 

FH,  F(CH3),  F3B,  F4Si, 
F5P,  &c. 

indirectly  :  very  undecided 
[from  sp.  ht.  of  CaF2,  &c.] 
directly 

metallic  fluorides  with  analogous 
compounds  of  Cl,  Br  and  I 
Na  compounds  with  those  of  other 
alkali  metals 

MAGNESIUM 

none 

directly 

Mg    compounds    generally   with' 

those  of  Zn,  Mn,  and  Fe  (in  fer- 

ALUMINIUM 

A1C13,  Al2Br6,  Al.,Ie 

directly 

rous  salts) 
with  Cr,  Mn,  and  Fe  in  R2O3  and. 

derivatives 

SILICON 
PHOSPHORUS 

SiF4,        SiCl4,        SiI4, 
Si(CH3)4,          SiH3Cl, 
Si2OCI6,  SijOCCoH,),, 
PH3.    PCI*    PI,,    PF.. 
POC13.    PSCI3)    P2I4, 

directly  :    sp.    ht.     varies    much 
with  temperature 

directly 

with  C,  Zr,  Sn,  and  Ti  in  com-> 
pounds  of  type  RO2 

phosphates   with    vanadates    andi 
arsenates,    organic     compounds! 

SULPHUR 

P2H4,  P3N3Cle,  &c. 
SH2,  SO.,,  S03,  SOU,, 
S2C,  S2U2,  &c. 

directly 

of  P  with  those  of  N,  As,  and  Sbl 
with    Se    compounds,    with     Te* 
compounds  of  type  RTe.     Saltst 
of  H2S04  with  those  of  H  ,Se04l 
and  H.,TeO4 

CHLORINE 

C1H,     C1(CH3),     C1T1, 

indirectly:  doubtful 

Chlorides,    with    analogous    conl-» 

CloZn,  CI2Hg.  C13HC, 
Cl3Bi,     Cl3Sb,     C14C, 
Cl4Si,     Cl4Ti,     Cl/la, 

[from  comparison  of  specific  heats 
of  various  haloid  compounds] 

pounds  of  Br  and  I 

CI5Mo,  C16W,  &c. 

POTASSIUM 

KI 

directly 

K  compounds  with  those  of  other 

alkali  metals 

CALCIUM 

none 

directly 

Ca  compounds  with  those  of  Sr,i 

Ba,  and  in  some  cases  Pb 

SCANDIUM 

none 

sp.  heats  of  some  compounds  de- 

[? Sc   compounds   with   those   of 

termined 

other  earth  metals] 

TITANIUM 

TiCl4 

directly 

TiO2  and  some  derivatives  withi 

analogous  compounds  of  C,   Si, 

Zr,  Sn,  and  Th 

VANADIUM 

VC14,  VOCI3 

sp.    heats   of   one   or   two    com- 

Vanadates  with   phosphates    aad» 

pounds  determined 

arsenates 

CHAP.  I.  §  38]     COMBINING   AND   ATOMIC   WEIGHTS. 

Atomic   Weights  of  the  Elements. 


V                                                  VI                                     VII 

VIII 

Atomic  weight 

(0                (2) 

ty  vapotn 
density 
method 

by  sp.  heat 
method 

Compounds  analysed,  &c. 
in  order  to  find  combining    Combining 
weight  of  the  elemettt         ,     weight 

Remarks 

or  more  details  concern-  1 

Tables,  pp.  39  —  44  and               [See  note  B,  p.  92.] 

[See  note  C,  p.  92. 

PP-  5I-53-]                 ^ 

7  -QI           •  Lithium  chloride 

7-01 

9-08                  9-08           2  Beryllium  sulphate 

4'54 

io'95                io'9s          3  Borax,  boron  chloride 

3-65 

11-97 

11-97       !    4  Diamond  burnt  to  CO2 

2'99 

5  Ammonium     chloride,     silver 

4-67 

nitrate 

'5-96 

— 

6  Synthesis  of  water 

7-98 

19*1 

1    1  Sodium     fluoride,     potassium 

I9'1 

fluoride,  calcium  fluoride 

23 

8  Sodium  chloride 

23 

24 

9  Magnesium      sulphate,       do. 
chloride,   synthesis   of    macr- 

12 

nesium  sulphate 

27'O2                         27'O2 

10  Ammonia     alum       aluminium 

9  '007 

bromide,  solution  of  alumin- 

ium in  soda 

28'3                  28*3            "  Silicon  chloride;  decomposition 
of  silicon  bromide  by  water 

7'o8 

30-96       i         30-96          12  Phosphorus  chloride,  synthesis 
of  phosphorus  pentoxide 

'°'3'    : 

31-98               31*98       i  I3  Synthesis   of   silver   sulphide, 

10-66 

reduction   of  silver  .sulphate 

by  hydrogen 

35'37 



14  Potassium   chlorate,   synthesis 
of  silver  chloride 

35'37 

39  04                39°°4          l5  Potassium   chloride,    do.    bro- 

39  '°4 

mide 



39'9           le  Calcium  chloride,  calcium  car- 

'9'95 

bonate 





17  Synthesis    of    scandium     sul- 

14-68 

Sc.     The  atomic  weight  of  this  metal 

48 

48 

phate 
18  Titanium     chloride,     bromide 

12 

is  most  probably  I4'68X3  =  44'04:  if 
this  is  so,  the  oxide  is  ScsO3,  and  is 

and  oxide 

analogous   with   the   oxides  of   the 

earth  metals. 

51  '2 



19  Vanadium  pentoxide,  do.  oxy- 
chloride 

.  12-8 

88 


ATOMS   AND   MOLECULES. 
Atomic  Weights  of  the  Elements. 


[BOOK  I. 


I 

11 

III 

IV 

Element 

Principal  compounds, 
vapour  densities  of 
•which  have  been 
determined 

Specific  heat  : 
how  determined 

Isomorphism  : 
compounds  compared 

[See  note  A,  p.  92.] 

CHROMIUM 

CrO2Cl2,  CrCl3 

directly  [?  too  low] 

Salts  of    H2CrO4  with   those   of 
H2Mn04    and    H2TeO4,    Cr2O3 
with  A1,O3  Mn2O3  and  Fe2O3 

MANGANESE 

MnCl2 

directly  [?  too  high] 

VIn2O3    with    AUO3    Cr2O3   and 
Fe203>    R,MnO"4   with    R2CrO4 
and     R2Te04,     RMnO4     with 

RC1O4 

IRON 

Fe2Cl6 

directly 

Fe2O,  and  derivatives  with  Al2Oj 
Cr,63   Mn2O3  and   derivatives, 

some  Fe  salts  with  those  of  Ni 

Co  and  Cu 

NICKEL 

none 

directly 

Ni  with  Co  compounds,  some  Ni 

compounds   with    those    of   Fe 

(ferrous  salts) 

COBALT 

none 

directly 

Co  with  Ni  compounds,  some  Co 

compounds    with    those    of    Fe< 

(ferrous  salts) 

COPPER 

Cu2Cl2 

directly 

most  Cu  compounds  with  those  of 

Ni  and  Co,  some  with  Fe  (fer- 

rous)  compounds,   Cu  with   Ag  , 

ZINC 

ZnCl,,  H  Zn(CH3)2) 

directly 

compounds  of  type  R2O 
Zn  compounds  with  those  of  Mgi 
and  Mn 

GALLIUM 

Ga2Cle 

directly  [?  too  low] 

Ga  alum  with  other  alums 

GERMANIUM 

GeCl4)  GeI4,  GeS 

directly:  sp.  heat  becomes  con- 

ARSENIC 

AsH3,       AsCl3,      AsI3, 
As(CH3)2Cl,       As4O6, 
&c. 

stant  only  at  high  temperature 
directly 

As  compounds  with  those  of  $> 
and   Bi,   organic    compounds   of 
As  with  those  of  N  P  and  Sb, 

arsenates  with   phosphates   and 

vanadates 

SELENION 

SeH,,  SeO2 

directly 

Se  with  S  compounds 

BROMINE 

BrH.   Br(CH3),    Br2Cd, 

directly 

Bromides    with    analogous    com- 

Br3B, Br4Sn,  Br4U,  &c. 

pounds  of  Cl  and  I 

RUBIDIUM 

RbCl,  Rbl 

indirectly  :  doubtful 
[from  comparison  of  specific  heats 

Rb  compounds  with  those  of  other 
alkali  metals 

of  some  compounds  with  those 
of  other  alkali  metals] 

STRONTIUM 

none 

indirectly:  doubtful 

Sr  compounds  with  those  of  Ca 

[comparison  of  specific  heats  ol 

and  Ba,  and  with  some  Pb  salts 

compounds  of  Sr,  Ca,  and  Ba] 

YTTRIUM 

none 

sp.  heats  of  a  few  compounds  de- 

Yt compounds  with  those  of  other 

termined 

earth  metals 

ZIRCONIUM 

ZrCl4 

directly  [?  too  low] 

ZrO2  with  TiO2  ThO2  SnO2  and 

SiO2 

NIOBIUM 

NbCIj.  NbOClj 



Nb  with  Ta  compounds,  Nb  flu- 

orides and  oxyfluorides  with  Mo 

do.  do. 

MOLYBDENUM 

MoCle 

directly  [?  too  high] 

Mo    with    W    compounds,    some 
salts  of  H2MoO4  with  those  of 
HXrO,.  Mo  with  Xb  fluorides 

and  oxyfluorides 

CHAP.  I.  §38]    COMBINING   AND   ATOMIC   WEIGHTS. 
Atomic  Weights  of  the  Elements. 


V                                                  VI                                     VII 

VIII 

Atomic  weight 

(i) 

(2) 

>y  vapour 
density 
method 

by  sp.  heat     Compounds  analysed  &~c. 
*   r,,     ,        in  order  to  find  combining 
weight  of  the  element 

Combining 
weight 

Remarks 

or  more  details  concern- 
ing these  numbers  see 

[See  note  C,  p.  92.] 

Tables,  pp.  39—44  and                [See  note  B,  p.  92.] 

PP-  5I—53-] 

52-4                 52-4         j  20  Chromium      chloride,     silver 

26-2 

chromate,   potassium  dichro-  j 

mate 

55                     55               21  Manganese  chloride,  mangan- 

27-5 

ous-manganic     oxide,     man- 

ganous    oxalate,    silver    per- 

manganate, &c. 

55'9 

55-9           22  Synthesis     of     ferric     oxide, 

27-95 

[see  p.  60] 

reduction     of     ferric     oxide. 

j 

analysis  of  ferrous  and  ferric 

J 

chlorides 



58-6 

23  Nickel  chloride,  nickelous  ox- 

29*3 

ide,  strychnine-nickel  cyanide 

brucine-nickel  cyanide,  &c. 



59 

21  Ammonium  -cobalt       cyanide, 

29'5 

phenyl-ammonium  cobalt  cy- 

anide,   strychnine    and    bru- 

cine-cobalt  cyanides 

63-4 

63-4 

25  Reduction    of    copper    oxide, 

3i  '7 

[see  p.  60] 

electrolysis     of     copper     sul- 

phate, &c. 

65-48 

65-48 

26  Synthesis  of  zinc  oxide,  analy- 
sis of  potassium-zinc  chloride, 

32-74 

solution  of  zinc  in  acid 

69 

69 

27  Oxidation  of  the  metal,  analy- 

23 

[see  p.  60] 

sis  of  gallium-ammonia  alum 

72-3 

72'3 

"a  Germanium  chloride 

18-08 

74'9 

74'9 

28  Arsenic  bromide,  do.  chloride, 

24-97 

do.  oxide 

78-8 

78-8 

29  Reduction  of  selenion  dioxide. 

39  '4 

reduction  of  silver  selenite 

79'75 

79-75          30  Synthesis    of   silver   bromide,           70/75 

analysis  of  potassium  bromide 

85-2 

31  Rubidium  chloride 

85-2 

— 

— 

32  Strontium  chloride 

„„ 

Sr.     The  atomic  weight  of  strontium 
must   be  taken  as  43-65X2  =  87-3  if 
the  formulas  of  its  salts  are  to  be- 

come  analogous  to  those  of  the  Ba 

and  Ca  salts. 





33  Synthesis  of  yttrium  sulphate             29-87        ;  Yt.     Atomic  weight  probably  =20/?7 
;      x  3  =  80-6  because  of  analogy  orYt 

salts  with  those  of  the  earth  metals. 

90 

90 

34  Zirconium  chloride,  potassium            45 
zh-conium  fluoride 

94 



3S  Niobium  chloride,  potassium-           31  '32 

niobium  oxyfluoride 

95'8 

95'8 

3B  Molybdenum  dichloride,  tetra            19-16 
chloride,  and  pentachloride 

ATOMS   AND   MOLECULES. 
Atomic  Weights  of  the  Elements. 


[BOOK  i. 


I 

II 

III 

IV 

Principal  compounds, 

Element 

vapour  densities  of 
which  have  been 

Specific  heat  :                            Isomorphism  : 
how  determined                    compounds  compared 

determined 

[See  note  A,  p.  yt.] 

RHODIUM 

none 

directly 

most  Rh  compounds  with  those  c- 
Ru,  Pd,  Ir,  Pt,  and  Os 

RUTHENIUM 

none 

directly 

most  Ru  compounds  with  those  o 

Rh,  Pd,  Ir.  Pt.  and  Os 

PALLADIUM 

none 

directly                                                  most  Pd  compounds  with  those  01 

Ru,  Rh,  Ir,  Pt,  and  Os 

SILVER 

AgCl 

directly                                                '  some  Ag  compounds  with  those  o 

Na  and  other  alkali  metals.  A* 

with    Cu    compounds    of    tvp<> 

R2O,  a  few  Ag  and   Au  com» 

pounds 

CADMIUM 

CdBr8 

directly 

some  Cd  compounds  with  those  o« 

Be  and  Zn 

INDIUM 

InCI3 

directly 

some  In  compounds  with  those  O* 
Cd  and  He 

TIN 

SnClj,  SnCl4,  Sn2Cl4 

directly 

SnO2  with  TiO2  ZrO2  and  ThOt, 

ANTIMONY 

SbCl3,      SbI3>      SbBr3, 
Sb(CH3)3,  Sb40, 

directly 

Sb  compounds  with  those  of  A* 
and  Bi 

TELLURIUM 

TeH2,  TeCl4,  TeCl2 

directly 

most  Te   compounds  with   those* 

ofSandSe 

IODINE 

IH,  Id,  KCHj),  \^t, 

directly 

Iodides    with     analogous     conw 
pounds  of  Cl  and  Br 

CAESIUM 

CsCl,2CsIC' 

indirectly:  doubtful 
[comparison  of  specific  heats  of 

Cs  compounds  with  those  of  others 
metals  of  alkalis 

compounds  with  those  of  other 

alkali  metals] 

BARIUM 

none 

indirectly  :  doubtful 

Ba  compounds  with  those  of  QU 

[comparison  of  specific  heats  of 

andSr 

LANTHANUM 

none 

compounds  of  Ca,  Sr,  and  Ba] 
directly                                            ^j 

CERIUM 

none 

directly 

most  La  compounds  with  those  « 

DIDYMIUM 

none 

directly 

Ce,  Di,  Kr  and  Yt,  some  coift-» 
pounds  of  these  metals  with  Ca» 

ERBIUM 

none 

sp.  heats  of  a  few  compounds 

compounds 

determined 

YTTERBIUM 

none 

sp.    heats  of   a   few  compounds 
determined 

[?  a  few  Yb  compounds  with  those*, 
of  other  earth  metals] 

TANTALUM 

Tads 

Ta  with  Nb  compounds 

TUNGSTEN 
IRIDIUM 

WOCI4>  WClj,  WC16 
none 

directly 
directly                                             ^ 

W    with    Mo    compounds,   some« 
salts  of  H2WO4  with  those  of' 
H2CrO4  and  H2TeO4 

OSMIUM 

OsO4 

directly                                             t 

Os,   Ir,  and  Pt,  compounds  withf 
those  of  Ru,  Rh,  and  Pd 

PLATINUM 

none 

directly                                          ) 

CHAP.  I.  §38]       COMBINING   AND   ATOMIC   WEIGHTS. 
Atomic  Weights  of  the  Elements. 


V 

VI 

VII 

VIII 

Atomic  weight 

(i) 

(2) 

y  vapour 
density 
method 

by  sp.  heat 
method 

Compounds  analysed,  &>c. 
in  order  to  find  combining 
weight  of  the  element 

Combining 
weight 

Remarks 

or  more  details  concern- 

ing these  numbers  see 

[See  note  C.  p.  92.] 

Tables,  pp.  39—44  and 

[See  note  B,  p.  92.] 

PP-  5I—53-]             f 



104 

37  Potassium-rhodium  chloride 

26 

(103) 

(37a  Purpureo-rhodium  chloro-and 

(25-75) 

bromo-compounds) 



I04'5 
106-2 

39  Palladium  chloride 

26-55 

107-66 

107  '66 

40  Silver  chlorate,  bromate,  iodate, 

107-66 

synthesis  of   silver   bromide 

and  iodide 

112 

112 

41  Cadmium  bromide 

56 

"3  '4 

"3'4 

42  Synthesis  of  indium  oxide 

37-8 

117-8 

II7-8 

43  Synthesis  of  stannic  oxide 

58-9 

120 

120 

44  Antimony  bromide,   reduction 

4O 

of  antimony  oxide,  also  analy 

sis  of  antimony  sulphide 

125 

125 

45  Oxidation  of  tellurium,  analy- 

62-5 

sis     of    potassium-  tellurium 

bromide,   synthesis   of    basic 

126-53 

126-53 

tellurium  sulphate  and  of  cop- 
per telluride 
"Silver    iodate,     silver    iodide, 

126-53 

synthesis  of  do. 

I32-7 



47  Caesium  chloride 

«3--7 



— 

48  Barium  chloride 

68-43 

Ba.    Atomic  weight    probably  68-43 
X2=  136-86  because  of  analogies  be- 

tween salts  of  Ba,  Sr,  and  Ca. 



I38-5 

49  Lanthanum   sulphate,  do.   ox- 

46-17 

ide,  do.  oxalale 



1  39  '9 

50  Cerium  oxalate,  do.  chloride, 

46-66 

do.  sulphate 



144 

51  Didymium  oxide  and  sulphate 

48 

(142) 

(47-6) 



52  Erbium  sulphate 

55^3 

Er.    This  metal  belongs  to  the  earth 
group,  hence  the  atomic  weight  is 

taken  as  55  -33X3  =  166. 





53  Ytterbium  sulphate 

57-69 

Yb.     For    similar    reasons    to    those 
which  apply  in  cases  of  Sc,  Yt,  and 

182 



54  Potassium  -tantalum     fluoride. 

60-67 

Er,  the  atomic  weight  of  Ytterbium 
is  regarded  as  3  times  its  combining 

183-6       ;         183-6 

55  Reduction    of    tungstic   oxide. 

30-6 

weight  (=173). 

analysis  of  tungsten  hexachlor- 

ide 



HP'S 

56  Potassium-iridium  chloride 

48-13 

*93 

T93 

57  Osmium  tetroxide 

48-25 

Os.    The  number  given  is  calculated 

from    2    determinations    of   vapour 

I94-3 

58  Potassium  -platinum   chloride,           48-57 
platinum     tetrachloride     and  ' 

density    of    OsO4    by   Deville    and 
Debray,    other  experimenters   have 

bromide,  &c. 

!     found  numbers  for  the  atomic  weight 

of  this  metal  varying  from  195  to  199. 

92 


ATOMS   AND   MOLECULES. 
Atomic  Weights  of  the  Elements. 


[BOOK  I. 


I 

II 

III 

IV 

Element 

Principal  compounds, 
•vapour  densities  of 
which  have  been 

Specific  heat: 
how  determined 

Isomorphism  : 
compounds  compared   '••. 

determined 

[See  note  A,  p.  92.] 

GOLD                    !  none 

directly 

some  Au  compounds  with  those  o 
Ag,  a  few  Au  compounds  witV 

those  of  Ni  and  Fe 

MERCURY         |[HgC,]HHga2(    HgI2, 

directly 

Hg  and  Cu   compounds  of  typ 

THALLIUM 

T1C1 

directly 

Tl  compounds  with  those   of  PI 
of  type  RC12,  Tl  compounds  0 
type  T1C1  with  those  of  alkal 

metals 

LEAD 

PbCl2,  Pb(CH3)4                  directly 

some  Ph  with  Tl  compounds,  man* 
Pb  with  Cu  and  Hg  compouS 

BISMUTH 

BiCl3                                     directly 

Bi  compounds  with  those  of  • 

andSb 

THORIUM 

ThCl4 

directly 

ThOa  with  SiO2  TiO2  SnO,  M 

URANIUM 

UC14,  UBr4                          directly 

some   compounds  of  type   Ufl 
with  those  of  Al,  Cr,  Mn,  all 

Fe 

Notes  to   Table  of  Atomic   Weights. 

A.  As  the  method  based  on  isomorphism  of  compounds  is  chiefly  used  as 
a  means  of  verifying  values  assigned  to  atomic  weights  by  other  methods,  no 
numbers  are  given  in  column  IV.,  but  merely  an  indication  of  the  various  com- 
pounds which  have  been  compared  crystallographically,  and  on  which  arguments 
for  or  against  a  given  value  for  the  atomic  weights  in  column  V.  have  been,  or 
may  be,  based. 

B.  This  column  (vi.)  is  not  to  be  regarded  as  containing  anything  like  a 
complete  summary  of  the   processes   employed   for  determining  the  combining 
numbers  of  the  elements ;   only  the  more  important  processes  are  indicated ; — 
references  are  given  to  the  original  papers.     References  to  the  papers  on  the 
spec,  heats  of  the  elements  will  be  found  on  pp.  53—54. 

A  complete  account  of  all  researches  on  this  subject  will  be  found  in  A  Re- 
calculation of  the  Atomic  Weights,  by  F.  W.  Clarke  [Part  V.  of  the  Constants  of 
Nature  published  by  the  Smithsonian  Institution],  and  also  in  Die  Atomgewichte 
der  Elemente,  by  L.  Meyer  and  K.  Seubert  [Leipzig,  1883]. 

C.  When  the  atomic  weight  given  in  column  v.  section  (2)  is  a  multiple  of 
the  combining  number  in  column  vn.,  no  number  being  given  in  section  (i)  of 
column  v.,  it  is  to  be  inferred  that,  besides  the  argument  drawn  from  the  value 
of  the  specific  heat  of  the  element  in  question,  there  are  other  chemical  reasons 
for  adopting  the  special  multiple  which  appears  in  V.  (2).     These  reasons  may  be 
broadly  described  as  based  on  analogies  between  salts  of  the  given  element  and 
salts  of  other  elements  the  atomic  weights  of  which  have  been  established  by  the 
two  leading  physical  methods. 


CHAP.  I.  §  38]     COMBINING  AND  ATOMIC  WEIGHTS. 
Atomic  Weights  of  the  Elements. 


93 


V 

VI 

VII 

VIII 

Atomic  weight 

(i)                 (=) 

;/Sy7    by  sp.  heat 

Compotinds  analysed,  &^c. 
in  order  to  find  combining 
weight  of  the  element 

Combining 
weight 

Remarks 

>r  more  details  concern- 

ing these  numbers  see 

[See  note  C,  p.  92.] 

Tables,  pp.  39  —  44  and 

[See  note  B,  p.  92.] 

PP-  5i—  53-1             f 

199-8 
203-64 


199-8 

203-64 


59  Gold  chloride,  potassium-gold  65-66 

chloride,  potassium-gold  bro 
mide 

60  Mercuric  chloride,  do.  oxide      !        99*9 


Synthesis  of  thallium  nitrate 


203-64 


206-4 
208 


231-87 
240 


62  Synthesis  of  lead  nitrate,  do.  |       103-2 

do.  sulphate 

63  Synthesis  of  bismuthous  oxide,  69-33 

&c.,  analysis  of  bismuthous 
chloride 

64  Thorium  sulphate 


65  Uranium  acetate,  do.  oxalate 


57'97 
60 


References  to  Table  of  Atomic   Weights. 

1  Li.    J.   W.  MALLET,  Sill.  Amer.  Journal  (2)  22.   349.     STAS,   Nouvelles 
Recherches,  pp.  268  and  274. 

2  Be.    NILSON  and  PETTERSSON,  Ber.  13.  1451. 

3  B.    BERZELIUS,  Pogg.  Ann.  2.  129.   DEVILLE,  Ann.  Chim.Phys.  (3)55. 180. 

4  C.     DUMAS  and   STAS,  Ann.   Chim.    Phys.    (3)    1.    5.     ERDMANN    and 
MARCHAND,  J.  fur prakt.  Chemie.  23.  159.     ROSCOE,  Compt.  rend.  94.  1180. 

5  N.     STAS,  Rapports,  pp.  50,  87,  92;  and  Nouvelles  Recherches,  pp.  57,  281. 

6  0.    ERDMANN  and  MARCHAND,  J.  fiir  prakt.  Chemie,  26.  468.     DUMAS, 
Ann.  Chim.  Phys.  (3)  8.  189.     KEISER,  Ber.  20.  2323.     COOKE  and  RICHARDS, 
Proc.  Amer.  Acad.  of  Arts  and  Sci.  23.  149. 

7  F.     LOUYET,  Ann.    Chim.    Phys.    (3)  25.   291.     DUMAS,  do.   (3)  55.    170. 
DE  LUCA,  Compt.  rend.  51.  299. 

8  Na.     PELOUZE,  Compt.  rend.  20.  1050.     DUMAS,  Ann.  Chim.  Phys.  (3)  55. 
182.     STAS,  Rapports,  p.  78;  and  Nouvelles  Recherches,  p.  248. 

9  Mg.     JACQUELAIN,  Ann.  Chim.  Phys.  (3)  32.   202.     BAHR,  J.  fiir  prakt. 
Chemie,  56.  310.     DUMAS,  Ann.  Chim.  Phys.  (3)  55.  187.     MARIGNAC,  Archiv. 
Scien.  Phys.  nat.  (3)  10.  5,  193. 

10  Al.    J.  W.  MALLET,  Phil.  Trans,  for  1880.  1003  et  seq. 

11  Si.     PELOUZE,  Compt.  rend.  20.  1052.  DUMAS,  Ann.  Chim.  Phys.  (3)  55.  183. 
J.  SCHIEL,  Annalen,  120.  94.     THORPE  and  YOUNG,  C.  S.  Journal,  51.  576. 

12  P.     PELOUZE,  Compt.  rend.  20.  1053.     SCHROTTER,  Ann.  Chim.  Phys.  (3) 
38.  131.     DUMAS,  Ann.  Chim.  Phys.  (3)  55.  172. 

13  S.     STAS,  Rapports,  p.  53. 


94  ATOMS   AND    MOLECULES.  [BOOK  I. 

14  Cl.     STAS,  Rapports,  pp.  38,  42,  44,  118;  and  Nouvelles  Recherches,  p.  208. 

15  K.     STAS,  Rapports,  pp.  69,  91,  118;  and  Nouvelles  Recherches,  p.  244. 

16  <Ta.     BERZELIUS,  Pogg.  Ann.  8.  189.     DUMAS,  Ann.   Chim.  Phys.  (3)  55. 
190.   ERDMANN  and  MARCHAND,  ^««<z/<?«,  44.  216:  62.  210:  76.  219.   SALVETAL, 
Compt.  rend.  17.  318. 

17  Sc.     NILSON,  ^r.  13.  1439. 

18  Ti.     H.  ROSE,  Pogg.  Ann.  15.  145.     J.  PIERRE,  Ann.  Chim.  Phys.  (3)  20. 
257.     THORPE,  A?r.  16.   3014;   and    (in   full)  C.  S.  Journal,  Trans,  for  1885. 
108. 

19  V.     ROSCOE,  Phil.  Trans,  for  1868.  8,  23. 

20  Cr.     E.  PELIGOT,  Ann.  Chim.  Phys.  (3)  12.  528.     BERLIN,  Annalen,  56. 
207:  60.  108  et  seq.     F.  KESSLER,  Pogg.  Ann.  95.  211.     SIEWERT,  Zeitschrift 

fur  die  gesammten  Naturwissenschaflen,  17.  530. 

21  ^/w.     DUMAS,  Ann.  Chim.  Phys.  (3)  55.  150.     SCHNEIDER,  Pogg.  Ann. 
107.   605 :   Id.  Annalen,  113.    78.     DEWAR  and    SCOTT,    Proc.   R.    S.   35.   44. 
MARIGNAC,  Archiv.  Scien.  Phys.  not.  (3)  10.  5,  193. 

22  Fe.     BERZELIUS,  Annalen,  50.  432.    ERDMANN  and  MARCHAND,  Annalen, 
52.  212.    L.  E.  RIVOT,  Annalen,  78.  214.    DUMAS,  Ann.  Chim.  Phys  (3)  55.  157. 

23  Ni.     DUMAS,  Ann.  Chim.  Phys.  (3)  55.  149.     RUSSELL,  C.  S.  Journal  (2) 
1.  51:  7.  294.     SOMARUGA,  Fresenius's  Zcitschr.  6.  347.    R.  H.  LEE,  Ber.  4.  789. 
BAUBIGNY,  Compt.  rend.  97.  951. 

24  C0.     WESELSKY,  Ber.  2.  592.     R.  H.  LEE,  Ber.  4.  789.    RUSSELL,  loc.  cit. 

25  C~#.     BERZELIUS,  Pogg.  Ann.  8.  182.     ERDMANN  and  MARCHAND,  J.fiir 
prakt.  Chemie,  31.  391.     W.  HAMPE,  Fresenius's  Zeitschr.  13.  352.     BAUBIGNY, 
CVwz/A  rend.  97.  906.     RICHARDS,  /V0<r.  Atner.  Acad.  23.  177. 

26  Zn.     GAY-LUSSAC  and  THENARD,  Gilbert's  Annalen,  37.  460.    BERZELIUS, 
Pogg.  Ann.  8.  184.     ERDMANN,  Berzelius's  Lehrbuch,  (5th  ed.)  3.  1219.     P.  A. 
FAVRE,  Ann.   Chim.  Phys.  (3)  10.  163.     MARIGNAC,  Archiv.  Scien.  Phys.  nat. 
(3)  10.  5,  193.     REYNOLDS  and  RAMSAY,  C.  S.  Journal,  Trans,  for  1887.    854. 

-7  Ga.     LiiCOQ  DE  BOISBAUDRAN,  Compt.  rend.  86.  941. 
27a  Ge.     WINKLER,  J.fiir  prakt.  Chemie,  (2)  34.  177. 

28  As.     W.  WALLACE,  Phil.  Mag.  (4)  18.  279.     DUMAS,  Ann.  Chim.  Phys. 
(3)  55.  174.     F.  KESSLER,  Pogg.  Ann.  95.  204. 

29  Se.     PETTERSSON  and  EKMAN,  Ber.  9.  1210. 

30  Br.     STAS,  Nouvelles  Recherches,  pp.  158,  170  and  199. 

31  Jib.     BUNSEN,  Pogg.   Ann.   113.    339.     PICCARD,  J.  fiir  prakt.   Chemie, 
86.  453.     GODEFFROY,  Annalen,  181.  189. 

32  Sr.     MARIGNAC,  Annalen,  106.  168.    DUMAS,  Ann.  Chim.  Phys.  (3)66.  191. 

33  Yt.    CLEVE,  ^<?r.  6.  1467.     RAMMELSBERG,  Ber.  9.  1580. 

34  Zr.     HERMANN,  J.fiir  prakt.  Chemie,  31.  77.     MARIGNAC,  Ann.  Chim. 
Phys.  (3)  60.  257. 

35  Nl>.     MARIGNAC,  Fresenius's  Zeitschr.  5.  480. 

36  Mo.     P.  LIECHTI  and  B.  KEMPE,  Annalen,  169.  344. 

37  Rh.     BERZELIUS,  Pogg.  Ann.  13.  437. 

37»  Rh.    JORGENSEN,  J '.  fiir  prakt.  Chemie  (2)  27.  433. 

38  Ru.     CLAUS,  Pogg.  Ann.  65.  218. 

39  Pd.     BERZELIUS,  Pogg.  Ann.  13.  442. 

40  Ag.     STAS,  Rapports,  pp.  38,  42,  44;  and  Nouvelles  Recherches,  pp.   109, 
158,  171,  189,  193,  208. 


CHAP.  I.  §38]     COMBINING  AND  ATOMIC  WEIGHTS.  95 

41  Cd.     O.  W.   HUNTINGTON,   Proc.  Amer.  Acad.  of  Arts  and  Sd.  17.   28 
\_Chcm.  News,  44.  268]. 

42  /;/.     C.  WINKLER,  J.fiir prakt.  Chemie,  94.  8:  102.  282.     BUNSEN,  Pogg. 
Ann.  141.  28. 

43  Sn.     DUMAS,  Ann.  Chim.  Phys.  (3)  55.  154. 

44  Sb.     R.  SCHNEIDER,   Uber  das  Atomgewicht  des  Antimons  (Berlin),  1880. 
J.  P.  COOKE,  Proc.  Amer.  Acad.  of  Arts  and  Sci.  13.  i :  17.  13.    J.  BONGARTZ, 
Ber.  16.  1942. 

45  Te.     W.  L.  WILLS,  C.  S.  Journal,  Trans,  for  1879.  704.     BRAUNER,  Ber. 
16.  3055. 

46  /.     STAS,  Nouvelles  Recherches,  pp.  135,  152,  189,  193. 

47  Cs.     BUNSEN,  Pogg.  Ann.   119.    i.     JOHNSON  and  ALLEN,  Sill.  Amer. 
Journal,  (2)  35.  94.     R.  GoDEFFROY,  Annalen,  181.  185. 

48  Ba.     MARIGNAC,  Annalen,  68.  215.   DUMAS,  Ann.  Chim.  Phys.  (3)  55.  137. 

49  La.     MARIGNAC,  Ann.  Chim.  Phys.  (4)  30.  67.     CLEVE,  Bull.  Soc.  Chim. 
50.  212:  (2)  39.  151,  289.     BRAUNER,  C.  S.  Journal,  Trans,  for  1882.  75. 

50  Ce.     MARIGNAC,  Annalen,  68.  212.     H.  BUHRIG,  J.fiir  prakt.  Chemie  (2) 
12.   222.     ROBINSON,  Proc.  R.  S.  37.  150.     BRAUNER,  C.  S.  Journal,  Trans. 
for  1885.  879. 

51  Di.  B.  BRAUNER,  C.  S.  Journal,  Trans,  for  1882.  68. 
51a  Di.  P.  T.  CLEVE,  Bull.  Soc.  Chim.  (2)  39.  289. 

52  Er.  P.  T.  CLEVE,  Compt.  rend.  91.  381.     NILSON,  Ber.  13.  1459. 
5:J   Yb.  NILSON,  Ber.  12.  550:  13.  1430. 

54  Ta.     MARIGNAC,  Annalen,  Supplbd.  4.  351. 

55  IV.     ROSCOE,  Chem.  Neivs,  25.  61,  73. 

56  Ir.     K.  SEUBERT,  Ber.  11.  1767. 

57  Os.     DEVILLE  and  DEBRAY,  Ann.  Chim.  Phys.  (3)  56.  403. 

58  Pt.    K.  SEUBERT,  Ber.  14.  865.    [Annalen,  207.  29.]    W.  HALBERSTADT, 
Ber.  17.  2962. 

59  Au.     BERZELIUS,  Lehrbruch,  (5th  ed.)  3.  1212.    JAVAL,  Ann.  Chim.  Phys. 
17.  337.     LEVOL,  Ann.  Chim.  Phys.  (3)  30.  355.    THORPE  and  LAURIE,  C.  S. 
Journal,  51.  565. 

60  fig.     ERDMANN  and  MARCHAND,  J.  fur  prakt.  Chemie,  31.  392.     SVAN- 
BERG,  J.fiir  prakt.  Chemie,  45.  468.     MILLON,  Ann.  Chim.  Phys.  (3)  18.  345. 

C1   77.     W.  CROOKES,  Phil.  Trans,  for  1873.  277. 
K-  Pb.     STAS,  Rapports,  pp.  101  and  106. 

63  Bi.     SCHNEIDER,  Pogg.  Ann.  82.  303.     DUMAS,  Ann.  Chim.  Phys.  (3)  55. 
176.     MARIGNAC,  Archiv.  Scien.  Phys.  nat.    (3)  10.   5,  193.     Id.  Ann.   Chim. 
Phys.  (6).  i,  289.     LOWE,  Zeitschr.  anal.  Chemie,  22.  498.     SCHNEIDER,  J.fiir 
prakt.  Chemie,  (2)  30.  237. 

64  Th.     NILSON,  Ber.  15.  2527.     KRUSS  and  NILSON,  Ber.  20.  1665. 

65  U.     PELIGOT,  Ann.  Chim.  Phys.  (3)  20.  329. 

Note.  The  full  titles  of  Stas's  treatises  which  are  referred  to  in  this  table 
are :  ( i )  Recherches  sur  les  rapports  redproques  des  poids  atomiques,  par  J.  S.  Stas, 
Bruxelle;,  1860.  (2)  Nouvelles  recherches  sur  les  lots  des  proportions  chimiques, 
sur  les  poids  atomiques  et  leurs  rapports  mutuels,  par  J.  S.  Stas,  Bruxelles,  1865. 
A  translation  into  German  of  both  treatises  was  published  in  1867  under  the  title 
Untersuchungen  liber  (fie  Gcsetze  der  chemischen  Proportionen,  uber  die  Atomge- 
li'ichte  and  ihre  gegenscitigen  Verhdltnisse. 


[BOOK  i. 


CHAPTER  II. 


ATOMIC   AND   MOLECULAR   SYSTEMS. 


SECTION  I.     Nascent  Actions. 

39  WE  have  now  gained  the  conception  of  chemical  change 
as  consisting  in  the  interaction  of  molecules,  or  atomic 
aggregates.  The  molecules  are  sometimes  shattered  into 
parts  which  rearrange  themselves  to  form  new  molecules, 
or  aggregates  of  atoms ;  sometimes  new  and  more  complex 
molecules  are  formed  by  the  coalescence  or  combination  of 
less  complex  molecules. 

We  have  then  to  examine  the  properties  which  the  atoms 
of  elements,  and  the  molecules,  or  the  atomic  aggregates,  of 
elements  and  compounds,  exhibit  in  their  mutual  actions  and 
reactions. 

Can  a  distinction  be  based  on  chemical  facts  between  the 
atoms  and  the  molecules  of  elements  ? 

What  are  the  chemical  properties  of  the  atoms,  as  dis- 
tinguished from  the  molecules,  of  elements  ? 

When  answers  have  been  found  to  these  questions,  it  will 
then  be  necessary  to  examine  the  relations  between  the 
properties  of  molecules  and  the  properties  of  the  atoms  which 
compose  them. 

Brodie  applied  his  hypothesis  regarding  the  structure 
of  elementary  molecules  (see  ante,  p.  78,  par.  36)  to  explain  a 
number  of  phenomena  generally  grouped  together  under  the 


CHAP.  II.  §§39,40]         NASCENT   ACTIONS.  97 

name  nascent  actions.  That  explanation,  somewhat  simplified 
and  also  developed  by  subsequent  research,  is  usually  regarded 
as  the  most  satisfactory  that  can  be  given  in  the  present  state 
of  knowledge,  when  regard  is  paid  to  the  configurations  of 
the  systems  exhibiting  the  phenomena  in  question. 

When  hydrogen  is  passed  into  water  containing  silver 
chloride  in  suspension  no  chemical  change  occurs ;  when 
hydrogen  is  generated  in  the  vessel  which  contains  the  silver 
chloride  decomposition  of  this  salt  proceeds  rapidly  with  pro- 
duction of  silver  and  hydrochloric  acid.  Nitrobenzene  is  con- 
verted into  aniline  by  the  action  of  hydrogen  produced  in 
contact  with  it,  but  not  by  hydrogen  produced  in  another 
vessel  and  conducted  into  that  containing  the  nitrobenzene. 
Carbon,  hydrogen,  and  nitrogen  do  not  combine  directly; 
but  if  electric  sparks  are  passed  through  a  mixture  of  benzene 
vapour  and  nitrogen,  hydrocyanic  acid  is  produced.  Sulphur 
dioxide  and  water  when  heated  with  oxygen  are  only  very 
partially  changed  into  sulphuric  acid ;  but  if  the  oxygen  is 
produced  in  contact  with  the  moist  dioxide  (e.g.  by  decompo- 
sition of  nitrogen  trioxide)  the  change  into  sulphuric  acid  is 
rapidly  completed.  Sulphur  is  not  oxidised  to  sulphuric  acid 
by  bromine  in  presence  of  water ;  but  if  the  sulphur  is  pro- 
duced from  a  compound  in  presence  of  bromine  water,  it  is 
then  oxidised,  e.g.  sulphuretted  hydrogen  passed  into  bromine 
water  gives  hydrobromic  acid  and  sulphur,  and  also  sul- 
phuric acid.  Metallic  chlorides  (e.g.  aluminium  chloride) 
produced  by  the  action  of  metals  with  chlorine  only  at  very 
high  temperatures,  and  in  small  quantities  for  a  given  time 
of  action,  are  sometimes  much  more  easily  prepared  by  the 
action  of  chlorine  on  a  mixture  of  the  metallic  oxide  and 
carbon.  The  general  reaction  of  metals  with  dilute  cold  sul- 
phuric acid  is  to  produce  a  sulphate  and  evolve  hydrogen, 
but  with  nitric  acid  to  produce  a  nitrate  and  evolve  oxides  of 
nitrogen,  nitrogen,  or  ammonia  ;  many  metals  when  heated 
with  concentrated  sulphuric  acid  evolve  sulphur  dioxide,  either 
alone,  or  in  some  cases  mixed  with  hydrogen  and  sulphuretted 
hydrogen. 

40        These  phenomena,  and  many  others  of  the  same  class, 
M.  C.  7 


98  ATOMIC   AND   MOLECULAR   SYSTEMS.          [BOOK  I. 

find  a  partial  explanation  in  terms  of  the  molecular  theory, 
that  explanation  being  based  on  the  distinction,  already  in- 
sisted on,  between  molecules  and  atoms.  Any  mass  of  a 
gaseous  element  under  ordinary  conditions  is  built  up  of 
molecules,  but  if  we  assume  that  when  a  compound  molecule 
undergoes  decomposition  a  short  but  appreciable  time  elapses 
before  the  greater  number  of  the  elementary  atoms  which 
composed  it  have  rearranged  themselves  to  form  new  mole- 
cules, we  have  the  materials  for  a  fairly  satisfactory  explana- 
tion, from  one  point  of  view,  of  the  phenomena  of  nascent 
actions.  This  explanation  does  not  necessitate,  as  some  of 
its  opponents  say  it  does,  the  assumption  of  strange  and  in- 
explicable properties  as  belonging  to  the  elementary  atoms. 
Indeed  the  occurrence  of  the  phenomena  of  '  nascent  action ' 
seems  to  follow  as  a  necessary  deduction  from  the  molecular 
theory  applied  to  chemical  phenomena.  When  a  chemical 
reaction  occurs  between  two  molecules,  the  first  step  in  that 
process  must  in  very  many  cases  consist  in  a  breaking  up  of 
the  molecular  structures,  and  the  second,  in  a  rearrangement 
of  the  parts  of  the  molecules,  i.e.  of  the  atoms,  to  form  a  con- 
figuration stable  under  the  conditions  of  the  experiment :  and 
although  these  changes  occur  almost  simultaneously,  neverthe- 
less, if,  by  the  presentation  of  molecules  of  a  third  chemical 
substance,  there  is  rendered  possible  the  adoption  by  the 
various  atoms  of  another  configuration,  more  stable  than 
that  just  supposed  to  be  assumed,  this,  the  most  stable  con- 
figuration, will  be  adopted.  But  if  the  earlier  stable  con- 
figuration has  been  assumed  by  the  atoms,  it  does  not  follow 
that  the  introduction  of  the  third  class  of  molecules  will  now 
cause  this  configuration  to  become  unstable  \ 

1  It  may  be  urged  that  the  energy  or  part  of  the  energy  which  is  set  free 
during  the  mutual  actions  of  the  molecules  of  the  reacting  bodies,  instead  of 
being  run  down  to  the  form  of  heat  and  so  lost  to  the  system,  becomes  available 
for  performing  chemical  work  ;  and  that  the  only  difference  between  e.g.  ordinary 
and  'nascent'  hydrogen  is  to  be  found  in  the  greater  chemical  energy  of  the 
latter.  The  importance  of  this  point  of  view  is  of  course  admitted  by  the  up- 
holders of  the  atomic  explanation  of  nascent  actions,  but  they  would  supplement 
this  by  the  statement  that  the  configuration  with  which  the  greater  quantity  of 
energy  is  associated  is  atomic,  and  they  contrast  this  with  a  molecular  and  com- 
paratively inactive  configuration. 


CHAP.  II.  §  41]  NASCENT   ACTIONS.  99 

41  Following  out  this  line  of  argument,  it  would  appear 
probable  that  compounds  should  present  phenomena  some- 
what analogous  to  those  exhibited  by  elements  when  in  the 
nascent,  i.e.  on  the  hypothesis  now  adopted  the  atomic,  state. 
Let  it  be  supposed  that  no  chemical  change  occurred 
when  the  compound  molecules  a  and  b  were  brought  into 
contact,  nevertheless  if  the  atoms  constituting  these  molecules 
were  allowed  to  react  a  chemical  change  might  occur.  In  a 
reaction  wherein  any  given  compound  is  produced  there  must 
be  a  moment  of  time  when  this  compound  can  only  be  said 
to  exist  potentially,  when  the  atoms  which  constitute  its 
molecules  have  not  settled  down  into  stable  configurations; 
at  this  moment  the  compound  may  be  said  to  exist  in  the 
nascent  state.  If  the  atomic  vibrations  and  interactions  are 
allowed  to  run  what  may  be  called  their  normal  course,  the 
compound  molecules  are  certainly  produced,  but  if  these 
interactions  are  interfered  with,  a  new  set  of  molecules  may  be 
formed,  which  molecules  bear  a  more  or  less  simple  genetic 
relation  to  those  produced  in  the  normal  process  of  the 
chemical  change '. 

The  following  among  other  cases  of  chemical  change  find 
a  partial  explanation  in  terms  of  this  hypothesis.  Nitrous 
acid  has  no  action  on  the  primary  mononitroparaffins 
(CnH2n+1 .  NCX),  but  these  compounds  are  converted  into 
nitrolic  acids  (CBH2n .  N2O3)  by  the  action  of  potassium 
nitrite  and  sulphuric  acid,  i.e.  by  the  action  of  reagents  which 
by  their  mutual  decomposition  produce  nitrous  acid.  Nitric 

The  experiments  of  Victor  Meyer  on  iodine  give  direct  evidence  of  the 
separation  of  elementary  molecules  into  atoms  by  the  addition  of  energy  in  the 
form  of  heat.  (See  ante,  p.  33  par.  15.) 

In  Book  II.  chapter  II.  par.  189,  will  be  found  some  facts  regarding  dis- 
sociation which  bear  on  the  subject  of  nascent  actions. 

1  In  all  such  considerations  we  can  deal  with  molecular  phenomena  only  by  a 
statistical  method,  we  can  reason  only  as  to  the  average  condition  of  the  mass  of 
molecules  constituting  a  substance  at  any  moment  of  time. 

It  seems  not  improbable  that  there  may  sometimes  be  nearly  as  great 
differences  between  the  properties  of  a  number  of  elementary  atoms  all  of  one 
kind  and  the  elementary  molecules  which  are  produced  by  the  union  of  these 
atoms,  as  between  the  properties  of  a  number  of  atoms  of  different  kinds  and  the 
compound  molecules  produced  by  the  union  of  these  atoms. 

7—2 


IOO  ATOMIC   AND   MOLECULAR   SYSTEMS.  [BOOK  I. 

acid  does  not  act  on  napthol  to  produce  dinitronapthol,  but 
if  napthol  be  produced  in  contact  with  nitric  acid — e.g.  by 
boiling  diazonapthalene  hydrochloride  in  presence  of  nitric 
acid — dinitronapthol  is  formed.  Carbon  monoxide  and 
ethylene  do  not  react  to  form  acrolei'n  even  under  the  influence 
of  electric  sparks,  but  if  ethylene  is  exploded  with  a  quantity 
of  oxygen  less  than  sufficient  for  complete  oxidation,  carbon 
monoxide  is  produced  and  simultaneously  acrolei'n  is  formed, 
i.e.  the  chemical  change  proceeds  partly  in  its  normal  way 
and  at  the  same  time  the  'nascent'  carbon  oxide  interacts 
with  the  ethylene  with  production  of  acrolei'n.  When  para- 
iodophenol  is  fused  with  potash  at  163°  hydroquinone  is  pro- 
duced, but  at  higher  temperatures  only  resorcin  is  formed  : 
now  as  fusing  potash  does  not  act  on  hydroquinone  it  seems 
necessary  to  conclude,  that  in  the  fusion  of  paraiodophenol  at 
high  temperatures  hydroquinone  is  produced,  but  is  imme- 
diately changed  into  resorcin. 

42  Whether  the  course  of  a  chemical  action  is  or  is  not  to  be 
regarded  as  an  example  of  the  particular  application  of  the 
molecular  theory  now  under  consideration,  must  be  decided 
by  the  nature  of  the  change  in  question.  Some  of  the  changes 
which  occur  when  metals  and  acids  interact  probably  belong 
to  this  class  of  chemical  actions. 

The  products  of  the  mutual  actions  of  metals  and  sul- 
phuric and  nitric  acid,  respectively,  have  already  been 
broadly  stated.  That  no  hydrogen  is  evolved  in  the  case  of 
nitric  acid  is  generally  said  to  be  due  to  the  oxidation,  by 
the  nitric  acid,  of  the  atoms  of  hydrogen,  assumed  to  be  pro- 
duced by  the  interaction  of  the  metal  and  acid,  with  a  corre- 
sponding reduction  of  the  acid  to  oxides  of  nitrogen,  nitrogen, 
and  sometimes  ammonia. 

Direct  proof  in  favour  of  this  hypothesis,  in  the  case  of  the 
interaction  of  nitric  acid  and  magnesium,  has  been  given  by 
Gladstone  and  Tribe1,  who  have  shewn  that  when  a  small 
piece  of  magnesium  is  placed  in  a  large  excess  of  nitric  acid 
(strengths  I  :  I  and  I  :  2. — acid  to  water — were  employed)  the 
gas  at  first  evolved  consists  of  nearly  pure  hydrogen,  but 

1  C.  S.  Journal  Tram,  for  1879.  178. 


CHAP.  II.  §42]  REACTIONS  OF  ACIDS  WITH  METALS.  IOI 

that  oxides  of  nitrogen  are  very  quickly  produced.  The  same 
chemists1  have  established  a  close  relation  between  the  reac- 
tion with  sulphuric  and  nitric  acids  of  the  hydrogen  produced 
by  electrolysis  of  these  acids,  and  the  hydrogen  occluded  by 
platinum  or  palladium ;  they  have  also  shewn  that  hydrogen 
evolved  by  the  action  of  the  copper  zinc  couple  is  very 
analogous  in  general  reducing  actions  to  hydrogen  occluded 
by  platinum  or  palladium. 

When  concentrated  nitric  acid  is  subjected  to  electrolysis 
no  hydrogen  is  evolved,  but  the  acid  is  reduced;  when  more 
dilute  acid  is  used  hydrogen  is  evolved,  reduction  of  the  acid 
also  occurs,  and  the  more  rapid  the  electrolysis  the  greater  is 
the  quantity  of  hydrogen  evolved.  Concentrated  nitric  acid 
rapidly  acts  on  hydrogen  occluded  by  platinum  or  palladium, 
with  oxidation  of  the  hydrogen  and  reduction  of  the  acid. 
In  the  electrolysis  of  concentrated  sulphuric  acid  sulphur  is 
produced,  and  also  sulphur  dioxide  with  traces  of  sulphuretted 
hydrogen,  a  portion  of  the  hydrogen  formed  is  oxidised  and  a 
portion  escapes,  and  the  stronger  the  battery  power  the 
greater  is  the  quantity  of  hydrogen  evolved.  When  the 
electrolysis  is  extremely  slow,  no  hydrogen  is  evolved,  and 
sulphur  dioxide  is  produced  in  small  quantity  unmixed  with 
free  sulphur.  Hydrogen  occluded  by  palladium  or  platinum 
also  reduces  sulphuric  acid,  with  production  of  sulphur 
dioxide  and  escape  of  a  portion  of  the  hydrogen. 

Gladstone  and  Tribe  regard  the  metal  (platinum  or  palla- 
dium) present  in  their  experiments  as  instrumental  in  the 
chemical  change.  They  think  that  the  hydrogen  produced  is 
occluded  by  the  metal  and  again  given  off  to  the. acid,  and 
that  if  the  gas  is  produced  more  quickly  than  it  can  be 
occluded  the  excess  escapes  oxidation  by  the  acid :  it  is 
probable  that  occluded  hydrogen  forms  a  compound  with  the 
occluding  metal,  and  that  therefore  hydrogen  coming  from 
this  source  is  for  the  most  part  in  the  nascent,  i.e.  on  the 
present  hypothesis  the  atomic,  state.  Their  experiments  cer- 
tainly establish  the  fact  that  maximum  reduction  of  either 
acid  is  obtained  when  hydrogen  is  evolved  therein  near  an 

1   C.  S.  Journal  Trans,  for  1878.   139  and  306. 


102  ATOMIC  AND   MOLECULAR   SYSTEMS.         [BOOK  I. 

electro-negative  metal  ;  but  a  comparison  of  the  results  with 
occluded  and  electrolytically  evolved  hydrogen  shews  that 
the  reducing  action  of  the  latter  on  sulphuric  acid  is  more 
complete  than  that  of  the  former. 

There  are  two  hypotheses  regarding  the  mechanism  of  the 
changes  which  occur  when  metals  and  aqueous  solutions  of 
nitric  acid  interact.  One  hypothesis  asserts  that  these 
changes  generally  proceed  in  two  stages,  taking  place  simul- 
taneously ;  in  the  first  stage  the  metal  and  acid  react  to  pro- 
duce a  nitrate  and  hydrogen  ;  in  the  second  stage  the  hydro- 
gen, or  a  portion  of  it,  interacts  with  another  portion  of  the 
acid..to  produce  oxides  of  nitrogen,  ammonia,  or  nitrogen,  and 
water.  The  other  hypothesis  regards  the  various  gaseous 
products  as  direct  results  of  the  deoxidation  of  the  acid  by 
the  reaction  with  the  metal,  and  denies  that  hydrogen  is  pro- 
duced at  any  stage  of  the  process.  The  facts,  taken  as  a 
whole,  seem  to  me  to  be  more  in  keeping  with  the  first  than 
with  the  second  of  these  hypotheses.  Indeed  to  formulate  the 
reaction  of  zinc  and  nitric  acid  on  the  latter  hypothesis 
requires  that  nitric  acid  should  be  regarded  as  a  variable 
compound  of  nitrogen  pentoxide  and  water,  and  necessitates 
considerable  skill  in  the  manipulation  of  formulae1. 

The  interaction  of  copper  and  concentrated  sulphuric  acid 
has  been  studied  by  Pickering'2.  The  ease  with  which  this 
acid  undergoes  deoxidation  is  shewn  by  the  slow  production 
of  cuprous  sulphide  even  at  20°;  the  equation 


which  represents  the  change  as  consisting  in  deoxidation  of 
part  of  the  acid,  and  does  not  involve,  nor  according  to 
Pickering's  experiments  allow,  an  intermediate  stage  wherein 
hydrogen  reacts  with  the  acid,  is  nearly  realized  at  this  tem- 
perature. At  higher  temperatures  sulphur  dioxide  is  evolved, 
until  at  about  270°  the  action  consists  entirely  of  a  change 
which  may  be  formulated  as 


1  Deville,  Compt.  rend.  70,  20  and  550;  or  in  abstract,  Watt's  Diet.  Suppl.  2, 
304.     See  also  Acworth  and  Armstrong,  C.  S.  Journal,  vol.  2.  for  1877,  54  et  seq. 

2  C.  S.  Journal  TOM.  for  1878.  U2. 


CHAP.  II.  §42]  REACTIONS  OF  ACIDS  WITH  METALS.  103 

and   which   is   most    readily   explained   as   consisting  of  two 
parts  proceeding  simultaneously 

f(i)    Cu  +  H2SO4  =  CuSO4+H2\ 
\(')     H2+H2S04  =  2H20  +  S02J  ' 

Tin  and  lead  are  dissolved  by  hot  concentrated  sulphuric 
acid,  with  production  of  sulphates  and  evolution  of  hydrogen 
and  sulphur  dioxide,  sometimes  accompanied  by  sulphuretted 
hydrogen,  and  with  separation  of  sulphur.  With  more  dilute 
acid  tin  evolves  hydrogen,  and  as  temperature  is  increased, 
sulphuretted  hydrogen  also.  The  reaction  of  zinc  with  sul- 
phuric acid  is  broadly  analogous  to  that  of  tin:  with  pure  zinc 
and  very  concentrated  hot  acid,  the  products  are  hydregen 
and  sulphur  dioxide;  with  less  pure  zinc,  sulphuretted  hydro- 
gen and  sulphur  are  also  formed,  the  sulphur  compounds  (SO2 
and  SH2)  appearing  even  when  the  acid  is  very  dilute  and  is 
kept  cold  ;  with  moderately  dilute  pure  acid  and  pure  zinc 
hydrogen  is  the  only  gaseous  product  (s.  Pattison  Muir  and 
Adie,  C.  S.  Journal,  Trans.  1888,  47). 

Quantitative  analyses  of  the  products  of  reduction  of 
nitric  acid  by  magnesium,  zinc,  and  cadmium,  respectively 
shew  that  reduction  is  carried  furthest  by  magnesium,  and 
further  by  zinc  than  by  cadmium.  Now  the  'heats  of  for- 
mation '  (see  Chap.  IV.)  of  the  oxides  of  these  metals  are, 
for  Mg  147,132,  for  Zn  88,244,  and  for  Cd  30,364  thermal 
gram-units;  hence  in  these  cases  that  reaction  in  which  the 
greatest  amount  of  heat  is  produced  is  accompanied  by  the 
greatest  reduction  of  the  acid. 

The  following  numbers  representing  quantities  of  heat 
produced  in  the  chemical  changes  formulated  were  obtained 
by  Thomson*: — 

[H2,  S,  O4,  Aq]  =  2 10,760  gram-units  +. 

[H,  N,0\Aq]  =   34,270  „         +. 

[Zn,  H2SO4Aq]=  106,090  „         +. 

[Zn,2HNO3Aq]=  1 36,340  „         +. 

1  These  equations  tell  that  e.g.  when  2  grams  of  hydrogen,  32  grams  of 
sulphur,  and  64  grams  of  oxygen  interact  in  presence  of  a  large  quantity  of  water 
to  form  a  dilute  aqueous  solution  of  98  grams  of  sulphuric  acid,  210,760  gram- 
units  of  heat  are  produced.  (For  fuller  explanations  s.  Chap.  IV.) 


IO4  ATOMIC  AND   MOLECULAR   SYSTEMS.         [BOOK  I. 

Berthelot  gives  the  thermal  value  21,500  gram-units  to  the 
chemical  change 

HNO3Aq  (dilute) +  8H  =  NH,Aq  (dilute)  +  3H2O. 

From  these  numbers  we  should  expect  sulphuric  acid 
to  be  more  stable,  towards  heat,  than  nitric  acid,  and  we 
should  expect  the  reaction  of  zinc  with  these  acids  to  result 
in  a  more  complete  deoxidation  of  nitric  than  of  sulphuric 
acid. 

In  the  interaction  of  a  metal  with  nitric  acid  in  aqueous 
solution  at  ordinary  temperatures,  we  have  then,  an  unstable 
acid,  a  considerable  quantity  of  heat  produced,  and  the 
formation  of  hydrogen  in  contact  with  the  acid ;  we  have 
conditions  eminently  favourable  to  deoxidation.  In  the 
interaction  of  a  metal  with  dilute  sulphuric  acid,  on  the  other 
hand,  we  have  a  more  stable  acid  and  a  smaller  quantity  of 
heat  produced ;  the  hydrogen  escapes  unchanged ;  but  when 
the  acid  is  so  concentrated  that  addition  of  heat  from  with- 
out is  required  to  start  the  reaction,  and  when  the  acid  is 
therefore  in  a  condition  more  comparable  with  that  of  nitric 
acid  at  ordinary  temperatures,  a  portion  of  the  hydrogen 
then  evolved  undergoes  oxidation  at  the  expense  of  the 
oxygen  of  the  acid.  If  however  hydrogen  is  evolved,  as  in 
the  experiments  of  Gladstone  and  Tribe,  in  contact  with  the 
concentrated  acid  at  ordinary  temperatures,  a  part  of  this 
hydrogen  is  always  oxidised ' ;  this  shews  that  all  the  reacting 
substances,  and  also  the  conditions  of  the  reaction,  must  be 
considered,  and  that  attention  must  not  be  confined  to  the 
hydrogen  only. 

The  facts,  that  hot  sulphuric  acid  is  deoxidised  by  carbon, 
and  apparently  by  phosphorus  also2,  and  that  .it  is  possible 
by  heat  alone  to  decompose  this  acid  into  sulphur  dioxide, 
oxygen,  and  water,  have  caused  some  chemists  to  regard  the 
reactions  of  metals  with  this  acid  as  simply  cases  of  direct 
deoxidation:  but  it  seems  to  me  that  the  facts  enumerated — 
both  chemical  and  physical,  with  regard  to  the  interactions  of 

1  When  however  vapour   of  sulphuric    acid   mixed  ivith  hydrogen  is 
through  a  hot  tube,  sulphuretted  hydrogen  is  produced. 

2  Cross,  C.  S.  Journal  Trans,  for  1879.   253. 


CHAP.  II.  §42]  NASCENT   ACTIONS.  105 

metals  with  this  acid  and  with  nitric  acid — are  more  in 
keeping  with  that  hypothesis  according  to  which  hydro- 
gen plays  an  essential  part  in  the  series  of  changes,  than 
with  any  other  hitherto  advanced.  There  may  be,  indeed 
there  undoubtedly  is,  more  than  one  process  of  chemical 
change  resulting  in  the  deoxidation  of  sulphuric  acid  ;  in  some 
cases  direct  deoxidation  preponderates,  in  others  hydrogen 
plays  the  more  important  part. 

Experiments  conducted  by  Thorpe1  on  the  reducing 
action  of  zinc,  magnesium,  and  tin,  on  acidulated  solutions 
of  ferric  sulphate,  shewed  that  whatever  condition  tends  to 
give  greater  chances  of  contact  between  the  hydrogen  pro- 
duced in  the  liquid  and  the  ferric  sulphate  in  solution, 
increases  the  rate  of  reduction;  that  increase  of  the  rate 
at  which  hydrogen  is  evolved,  other  conditions  remaining 
constant,  is  accompanied  by  decrease  of  the  amount  of  re- 
duction in  unit  of  time;  and  that  the  presence  of  certain 
salts,  e.g.  zinc  sulphate,  causes  a  decrease  in  the  rate  of 
reduction.  Thorpe's  results  also  established  a  distinct 
connexion  between  the  nature  of  the  metal  used  and  the 
influence  on  the  rate  of  reduction  of  the  varying  conditions 
under  which  the  experiments  were  conducted. 

These  experiments,  and  indeed  all  experiments  oh  the 
interactions  of  metals  and  acids,  emphasise  the  necessity  that 
exists  for  considering  all  the  reacting  substances  which  take 
part  in  a  process  of  reduction  by  hydrogen,  and  not  confining 
attention  to  the  hydrogen  alone.  The  results  of  experiments 
by  Tommasi2  also  shew  this  need:  Tommasi  found  that  po- 
tassium chlorate  was  not  deoxidised  by  hydrogen  evolved  by 
the  action  of  sodium-amalgam,  but  was  reduced  by  hydrogen 
evolved  by  the  action  of  zinc  on  diluted  sulphuric  acid, 
but  that  the  latter  agents  failed  to  remove  oxygen  from 
potassium  perchlorate.  Experiments  conducted  in  my  la- 
boratory have  shewn  that  an  aqueous  solution  of  potassium 
chlorate  is  reduced  by  the  action  of  magnesium  or  sodium, 
and  by  that  of  the  copper-zinc  couple;  and  that  an  aqueous 

1  C.  S.  Journal  Trans,  for  1882.   289. 

2  See  especially  Pogg.  BeiWitter,  2.  205. 


106  ATOMIC   AND   MOLECULAR   SYSTEMS.          [BOOK  I. 

solution  of  potassium  perchlorate  is  very  slightly  reduced  (to 
chloride)  by  the  action  of  sodium,  and  by  the  prolonged  action 
of  magnesium,  but  is  not  reduced  by  the  action  of  the  copper- 
zinc  couple,  by  that  of  zinc  dust  and  potash,  or  by  electrolysis. 
43  The  conception  which  underlies  such  expressions  as  nascent 
actions,  action  of  nascent  hydrogen,  &c.,  is  that  implied  in  the 
distinction  drawn  between  atom  and  molecule.  That  this 
distinction  is  not  one  merely  of  terminology  but  is  based  on 
actual  reactions,  is  rendered  apparent  by  the  results  of  ex- 
periments by  Traube1  on  the  electrolysis  of  water,  using 
electrodes  of  different  materials.  For  instance,  he  found  that 
when  palladium  is  charged  with  hydrogen  and  made  the 
positive  pole  of  the  battery  no  hydrogen  peroxide  is  produced, 
but  the  oxygen  which  is  being  evolved  is  absorbed  by  the 
palladium  and  is  combined  with  the  occluded  hydrogen  to 
form  water.  When  however  the  hydrogenised  palladium  is 
made  the  negative  pole  a  little  hydrogen  peroxide  is  pro- 
duced; and  the  quantity  of  this  compound  may  be  con- 
siderably increased  by  causing  bubbles  of  air  to  rise  through 
the  liquid  near  the  negative  pole.  If  however  no  air  is  passed 
through  the  water,  and  at  the  same  time  the  transference  of 
oxygen  from  the  positive  pole  (where  it  is  being  liberated) 
through  the  liquid  to  the  negative  pole  is  mechanically  pre- 
vented, no  hydrogen  peroxide,  or  only  a  trace  of  this  com- 
pound, is  produced.  Further,  if  hydrogenised  palladium  is 
made  the  positive  pole,  and  bubbles  of  air  are  at  the  same 
time  caused  to  rise  through  the  liquid  around  the  pole,  a  little, 
but  only  a  little,  hydrogen  peroxide  is  produced. 

Finally  if  the  electrodes  are  made  of  palladium  uncharged 
with  hydrogen  the  maximum  yield  of  hydrogen  peroxide  is 
obtained  (entirely  at  the  negative  pole)  by  arranging  the  rate 
of  electrolysis  so  that  the  whole  of  the  hydrogen  produced  is 
occluded  by  the  palladium;  the  more  rapid  the  evolution  of 
hydrogen  from  the  liquid  the  smaller  is  the  quantity  of 
hydrogen  peroxide  produced2.  Now  it  is  generally  supposed 

1  £er,15.  659,  2421,  2434:  16.  1201. 

2  These  results  are  confirmatory  of  those  obtained  by  Gladstone  and  Tribe  in 
their  electrolytic  experiments  on  the  reduction  of  acids.     See  ante,  p.  100. 


CHAP.  II.  §§43,  44]         NASCENT   ACTIONS.  IO/ 

that  the  greater  part  of  the  oxygen  or  hydrogen  liberated 
during  the  electrolysis  of  water  is  at  the  moment  of  its  pro- 
duction in  the  state  of  atoms,  and  that  the  greater  part  of  the 
oxygen  in  ordinary  air  is  composed  of  molecules ;  if  this  be 
granted,  it  follows  that  Traube's  experiments  establish  a 
marked  difference  between  the  reactions  of  oxygen  atoms  and 
oxygen  molecules :  by  their  reaction  with  hydrogen  occluded 
by  palladium,  the  former  produce  water,  the  latter  produce 
hydrogen  peroxide;  if  a  few  atoms  and  many  molecules  of 
oxygen  are  present  much  peroxide  and  little  water  are  the 
products,  while  if  many  atoms  and  few  molecules  of  oxygen 
are  brought  into  contact  with  the  hydrogen,  much  water  and 
little  peroxide  is  the  result. 

44  But  the  experiments  of  Traube  also  shew  that  the  direction 
and  final  goal  of  the  chemical  change  depends  not  only  on  the 
structure  of  the  particles  of  oxygen,  but  also  on  the  source 
and  conditions  of  supply  of  the  hydrogen.  If  the  hydrogen 
is  produced  by  rapid  electrolysis  little  peroxide  is  formed; 
indeed  if  the  hydrogen  is  produced,  rapidly  or  slowly,  by 
electrolysis  with  carbon  poles  no  peroxide  is  obtained.  The 
chemical  nature  and  the  mass  of  each  of  the  members  of  the 
changing  system  influence  the  final  configuration.  The  im- 
portance of  considering  the  conditions  under  which  hydrogen 
is  produced  when  we  are  attempting  to  explain  any  of  the 
phenomena  classed  together  as  nascent,  is  emphasised  by  the 
fact  that  the  metals  which  decompose  water  in  absence  of  oxy- 
gen do  not  give  rise  to  the  production  of  hydrogen  peroxide 
by  their  action  on  water  in  presence  of  oxygen;  for  instance, 
hydrogen  peroxide  is  never  produced  by  the  action  of  sodium 
on  water.  It  is  not  enough  then  that  oxygen  molecules 
should  be  present  in  contact  with  atoms  of  hydrogen  as  these 
are  liberated  from  water.  The  peroxide  results  from  the 
mutual  interactions  of  the  three  substances,  metal,  water,  and 
oxygen;  if  the  water  is  decomposed  by  the  metal  alone, 
hydrogen  is  evolved  rapidly  and  escapes  the  pursuit  of  the 
oxygen  molecules;  the  peroxide  appears  to  be  a  product  of 
the  joint  action  of  the  metal  and  oxygen  on  the  molecules  of 
water. 


IO8  ATOMIC  AND   MOLECULAR   SYSTEMS.         [BOOK    I. 

The  conception  of  a  joint  action  of  metal  and  oxygen  with 
water  may  be  used  to  explain  some  of  the  phenomena  ex- 
hibited when  metals  and  acids  interact.  Traube  seeks  to 
explain  many  of  these  reactions  in  this  way. 

Copper  does  not  remove  oxygen  from  an  aqueous  solution 
of  potassium  nitrate  as  zinc  does:  but  if  copper  is  brought 
into  contact  with  dilute  sulphuric  acid  in  presence  of  oxygen, 
hydrogen  peroxide  is  produced.  The  joint  action  of  copper 
and  potassium  nitrate  is  not  sufficient  to  decompose  water- 
molecules  ;  but  copper  and  oxygen  aided  by  a  little  sulphuric 
acid  suffice  to  complete  this  change.  The  reaction  in  question 
is  represented  thus  by  Traube  :  — 

rOH  \H]  .....  7o  H-0 

(a)  Cu  +  \         I      \+\  |  =  Cu(OH)2  +          | 

(OH  j  HJ      lO  H-0 

(b)  (when  a  certain  amount  of  H2O2  is  produced) 

Cu  +  H202=Cu(OH)2 
(0     Cu(OH)2  +  H2S04=CuSO4  +  2H20. 

If  some  compound  which  is  readily  acted  on  by  hydrogen 
is  substituted  for  oxygen  in  this  series  of  changes,  then 
copper  and  dilute  sulphuric  acid  form  a  reducing  agent; 
ferric  sulphate  e.g.  is  reduced  under  these  conditions  to 
ferrous  sulphate:  — 

OH  fti"  ...... 

Cu  + 


Similarly  the  interaction  of  copper  with  dilute  nitric  acid 
would  be  represented  thus  :  — 


(OH  ;  H) 

]  U3(0  i  NO,H 

(OH  i  HJ         i 

[but  3NO2H  rapidly  decomposes  to  give  HNO3  +  2NO  +  H2O]. 

As  thus  regarded,  these  reactions  of  metals  with  acids  are 

complex  changes;   at   one   stage   or   other   of  the  complete 

change  hydrogen  plays  an  important  part,  and  it  does  this  in 

virtue  of  being  itself  a  product  of  another  part  of  the  whole 


CHAP.  II.  §§44, 45]         NASCENT   ACTIONS.  IOQ 

reaction.  Hydrogen  imported  from  without  the  system  fails 
to  accomplish  actions  which  are  brought  about  by  hydrogen 
generated  within  the  system,  provided  this  hydrogen  be  pro- 
duced at  the  proper  rate  and  under  conditions  generally 
favourable  to  the  action  it  is  to  perform. 

The  investigation  of  Divers1  'On  the  production  of  hy- 
droxylamine  from  nitric  acid'  is  an  interesting  and  instructive 
example  of  the  need  of  considering  all  the  members  of  a 
changing  system  in  attempting  to  find  an  explanation  of  the 
change.  Hydroxylamine  is  produced  in  very  small  quantities 
during  the  reaction  of  tin,  zinc,  and  some  other  metals,  with 
nitric  acid;  but  if  hydrochloric  or  sulphuric  acid  is  added  to 
the  zinc  and  nitric  acid  a  marked  increase  in  the  yield  of  hy- 
droxylamine  is  noticed.  When  a  mixture  of  nitric  and  sul- 
phuric acids  reacts  with  zinc  it  is  probable,  from  the  experiments 
made  by  Divers,  that  the  ammonia  which  is  produced  in  con- 
siderable quantities  is  a  product  of  the  direct  mutual  action  of 
the  zinc  and  nitric  acid,  and  that  the  hydroxylamine  is  a 
product  of  the  reduction  of  the  nitric  acid  by  the  combined 
interaction  with  that  acid  of  zinc  and  sulphuric  acid.  Zinc 
and  sulphuric  acid  in  presence  of  nitric  acid,  according  to 
Divers,  form  an  hydrogenising  mixture;  the  chief  products  of 
this  action  are  hydrogen  and  hydroxylamine,  besides  sulphate 
and  nitrate  of  zinc.  Zinc  and  aqueous  nitric  acid  alone  also 
form  an  hydrogenising  mixture;  but  the  chief  product  of  this 
action,  other  than  zinc  nitrate,  is  ammonia.  Hydroxylamine 
is  not  therefore  an  invariable  product  of  the  reaction  of  hy- 
drogen with  nitric  acid  even  when  that  hydrogen  is  evolved  in 
contact  with  the  acid  ;  it  is  rather  to  be  regarded  as  a  product 
of  the  combined  interaction  of  nitric  acid  and  sulphuric  acid 
with  zinc,  this  reaction  being  such  that  the  nitric  acid  is  sup- 
plied with  hydrogen  whereby  it  is  reduced  to  hydroxylamine. 
45  The  expression  'nascent  action'  has  probably  been  at  once 
helpful  and  harmful  to  the  progress  of  chemistry.  By  classing 
under  a  common  name  many  phenomena  that  might  other- 
wise have  been  lost  in  the  vast  mass  of  facts  with  which  the 


1  C.  S.  Journal,  Trans,  for  1883.  443 :  also  Divers  and  Shimidzu,  C.  S.  Journal, 
Trans,  for  1886.  597. 


110  ATOMIC   AND   MOLECULAR   SYSTEMS.          [HOOK  I. 

science  has  to  deal,  the  expression  has,  I  think,  done  good 
service;  but  in  so  far  as  its  use  has  tended  to  prevent  in- 
vestigation— for  it  is  always  easier  to  say  of  any  unusual 
reactions,  'these  are  cases  of  nascent  action,'  than  to  examine 
carefully  into  their  course  and  conditions — and  also  in  so 
far  as  it  has  favoured  the  impression  that  'nascent'  hydro- 
gen or  'nascent'  oxygen,  &c.  is  ordinary  hydrogen  or  oxygen, 
&c.  with  certain  indefinite  properties  which  always  belong 
to  the  hydrogen,  or  other  element,  when  in  this  peculiar  con- 
dition the  use  of  the  expression  has,  I  think,  been  unfavour- 
able to  the  best  interests  of  chemical  science. 

A  study  of  the  reactions  in  which  nascent  substances  play 
important  parts  appears  to  me  to  keep  before  the  student 
that  all-important  distinction  between  the  atom  and  the 
molecule  which  is  so  vital  in  chemical  considerations,  and  also 
to  draw  attention  in  a  marked  way  to  the  complexity  of  all 
chemical  changes.  We  find,  or  think  we  find,  that  when  atoms 
of  hydrogen  are  presented  to  another  substance  in  a  given 
chemical  reaction,  certain  definite  products  result;  and  we 
are  apt  to  conclude  that  the  interaction  of  hydrogen  atoms 
with  this  substance  will  always  give  this  result;  but  investi- 
gation discovers  that  not  only  the  course  of  the  reaction,  but 
also  the  final  configuration  of  the  changing  system,  is  de- 
pendent on  the  whole  previous  history  of  the  reacting  bodies. 
Hydrogen  as  it  is  produced  by  the  action  of  sodium-amalgam 
appears  to  possess  properties  different  from  those  which 
characterise  hydrogen  produced  by  the  reaction  of  zinc  with 
dilute  sulphuric  acid.  Attempts  to  explain  these  apparent 
differences  lead  to  fresh  researches;  the  results  of  these  re- 
searches shew  the  danger  of  using  such  an  expression  as  tJie 
properties  of  Jiydrogen  produced  by  the  action  of  sodium-amalgam, 
and  contrasting  these  with  the  properties  of  hydrogen  produced 
by  the  reaction  of  zinc  with  dilute  sulphuric  acid;  they  teach 
that  every  chemical  change  is  composed  of  parts,  and  that  the 
occurrence  of  one  part  is  dependent  on  the  occurrence  of  the 
other  parts,  that  we  cannot,  except  occasionally,  alter  one  part 
of  the  complete  change  and  expect  the  other  parts  to  proceed 
as  before,  The  change  of  hydrogen  and  potassium  chlorate 


CHAP.  II.  §§45,46]     USE   OF   TERM   'NASCENT.'  Ill 

in  aqueous  solution  to  potassium  chloride  and  water,  for 
instance,  is  dependent  not  only  on  the  interaction  of  the 
chlorate  and  hydrogen  but  also  on  the  interaction  whereby 
the  hydrogen  is  itself  produced.  It  is  not  that  hydrogen 
produced  in  one  way  has  certain  properties  and  hydrogen 
produced  in  another  way  has  other  properties,  but  rather  that 
the  members  of  the  system  composed  of  potassium  chlorate, 
water,  and  sodium-amalgam,  interact  to  produce  potassium 
chlorate,  soda,  water,  mercury,  and  hydrogen,  whereas  the 
members  of  the  system  composed  of  potassium  chlorate, 
water,  zinc,  and  sulphuric  acid,  interact  to  produce  potassium 
chloride,  water,  zinc  sulphate,  and  hydrogen.  We  thus  be- 
come impressed  with  the  conviction  that  chemistry  is  not  the 
study  of  this  element  or  that,  regarded  as  a  kind  of  matter 
with  certain  fixed  physical  properties,  but  that  processes  of 
change  are  the  subject-matter  of  the  science,  and  that  to 
explain  any  one  of  these  we  must  take  into  account  each  and 
all  of  the  reacting  bodies,  and  each  and  all  of  the  conditions 
under  which  the  total  change  is  proceeding. 

If  the  expression  'nascent  action'  does  in  any  way  help  to 
emphasise  such  considerations  as  these,  I  think  it  ought  to  be 
retained  in  chemical  nomenclature1. 


SECTION   II.     The  Dualist ic  and  Unitary  Hypotheses. 

We  must  now  examine  the  relations  between  the  chemical 
properties  of  atoms  and  of  the  molecules,  or  atomic  aggregates, 
which  are  formed  by  the  union  of  these  atoms.  We  must  in- 
quire whether  the  properties  of  the  molecule  are  the  sum  of 
the  properties  of  its  constituent  atoms ;  or  whether  the  latter 
properties  are  modified  by  the  mutual  interactions  of  the 
atoms.  We  must  endeavour  to  learn  something  regarding  the 
structure  of  molecules. 

46         Partly  from  his  definition  of  element,  partly  from  his  study 
of  the  products  of  combustion  in    oxygen,    of  phosphorus, 
carbon,  sulphur,  &c.,  Lavoisier  was  led  to  regard  every  salt 
1  See  also  Book  II.  chapter  n. 


112  ATOMIC   AND   MOLECULAR    SYSTEMS.          [BOOK  I. 

as  formed  by  the  union  of  an  acid  with  a  radicle,  the  latter 
being  itself  either  simple  or  compound. 

Davy  began  his  electro-chemical  researches  in  the  early 
years  of  the  present  century.  In  the  Philosophical  Transactions 
for  1807*,  and  in  his  Elements  of  Chemical  Philosophy*,  he 
regards  chemical  combination  as  accompanied  by  an  ex- 
change of  quantities  of  electricity  of  opposite  sign  between 
the  combining  bodies.  He  found  that  when  sulphur  and 
copper  are  rubbed  together  the  sulphur  is  negatively,  the 
copper  positively,  electrified;  and  that  when  the  sulphur  is 
heated  the  electrical  activities  become  more  apparent,  until 
the  sulphur  melts,  when  chemical  combination  occurs,  and 
the  product,  copper  sulphide,  exhibits  neither  positive  nor 
negative  electricity.  If  the  quantity  of  electricity  lost  in  the 
act  of  chemical  union  is  restored,  e.g.  by  the  passage  of  a 
current  through  the  compound  formed,  chemical  decom- 
position occurs  and  the  original  components  are  again  ob- 
tained. Davy  regarded  the  primary  cause  of  chemical  and 
electrical  effects  as  possibly  the  same  force;  when  this  force 
is  exerted  between  masses  of  matter,  electrical  phenomena,  he 
said,  result;  when  it  is  exerted  between  the  smallest  particles 
of  bodies  chemical  phenomena  result.  Thus  in  his  Elements 
of  Chemical  Philosophy*  Davy  says, 

"Electrical  effects  are  exhibited  by  the  same  bodies  when  acting  as 
masses,  which  produce  chemical  phenomena  when  acting  by  their  par- 
ticles ;  it  is  not  therefore  improbable  that  the  primary  cause  of  both  may 
be  the  same,  and  that  the  same  arrangements  of  matter,  or  the  same 
attracting  powers,  which  place  bodies  in  the  relations  of  positive  and 
negative,  i.e.  which  render  them  attractive  of  each  other  electrically,  and 
capable  of  communicating  attractive  powers  to  other  matter,  may  likewise 
render  their  particles  attractive,  and  enable  them  to  combine,  when  they 
have  full  freedom  of  motion."  "  That  the  decomposition  of  the  chemical 
agents  is  connected  with  the  energies  of  the  pile,  is  evident  from  all  the 
experiments  that  have  been  made;  as  yet  no  sound  objection  has  been 
urged  against  the  theory  that  the  contact  of  the  metals  destroys  the 
electrical  equilibrium,  and  that  the  chemical  changes  restore  it;  and,  in 

1  'On  some  chemical  agencies  of  electricity,' p.  i. 

3  Collected  Works,  vol.  iv.  (see  also  Ladenburg's  Entwickelungsgeschichte  der 
Chemie,  pp.  75—81). 

3  Pp.  119 — 1 20,  and  p.  125. 


CHAP.  II.  §47]    BERZELIUS'  ELECTRO-CHEMICAL  WORK.  I  13 

consequence,  that  the  action  exists  as  long  as  the  decompositions  con- 
tinue."1 

17  At  once  a  brilliant  theoriser  and  a  thorough-going  experi- 
menter, Davy  did  not  attempt  to  found  a  general  scheme  of 
chemical  classification  on  his  electro-chemical  work.  This 
was  however  done  by  Berzelius,  who  developed  a  consistent 
and  definite,  although  narrow,  theory  which  for  a  time  seemed 
to  explain  all  chemical  phenomena. 

All  chemical  actions  were  regarded  by  Berzelius  as  brought 
about  by  electrical  force2.  "Die  Elektricitat...scJieint  die  erste 
Thatigkeits-  Ursache  in  der  ganzen,  uns  umgebenden  Natur  zu 
sem."  Electrical  actions,  according  to  Berzelius,  were  not  to 
be  described  as  consequences  of  contact,  or  of  mutual  action, 
between  heterogeneous  bodies.  Each  elementary  atom,  he 
held,  is  endowed  with  two  kinds  of  electricity,  it  has  two 
electric  poles ;  but  these  poles  differ  in  strength,  so  that 
each  atom  considered  as  a  whole  is  positively  or  negatively 
electrified  ;  in  some  elementary  atoms  positive  electricity 
predominates  and  gives  a  positive  character  to  the  whole 
atom;  in  others  negative  electricity  overpowers  the  positive. 
When  a  positively  electrified  atom  attracts  a  negatively  elec- 
trified atom,  opposite  electricities  neutralise  one  another,  but 
the  electricities  formerly  masked  in  the  separate  atoms  now 
come  into  play,  and  so  the  new  group  of  atoms,  as  a  whole, 
exhibits  positive  or  negative  electricity,  in  virtue  of  which  it 
is  capable  of  chemically  combining  with  other  atoms  or  groups 
of  atoms.  But  as  the  stronger  poles  are  first  neutralised,  it 
follows  that  the  more  complex  a  compound  is,  the  less  polarity 
does  it  exhibit,  and  hence  the  less  readily  does  it  combine 
with  other  substances.  Berzelius  moreover  regarded  the  quan- 
tity of  electricity  on  either  pole  as  to  some  extent  variable 
with  variations  of  temperature.  By  the  Berzelian  theory 

1  It  is  interesting  to  observe  how  similar  this  view,  stated  by  Davy  in  the 
beginning  of  the  present  century,  is  to  the  latest  views  regarding  the  connexion 
of  chemical   and   electrical   forces.     Compare   especially   Helmholtz's    '  Faraday 
Lecture.'     (C.  S.  jfournal,  Trans,  for  1881,  277  et  seq.:  see  particularly  pp.  300 — 
302.)    [See /to/,  Book  II.] 

2  Lehrbuch  (ist  Ed.),  in.  part  I.  p.  77. 

M.C.  8 


114  ATOMIC   AND   MOLECULAR   SYSTEMS.         [BOOK  I. 

atoms  are  regarded  as  essentially  unipolar ;  one  polarity  so 
predominates  over  the  other  that  each  atom  acts  as  a  posi- 
tively or  negatively  electrified  whole. 

The  electro-chemical  properties  of  oxidised  compounds, 
Berzelius  taught,  depend  chiefly  on  the  unipolarity  of  the 
electro-positive  radicles  they  contain.  Of  two  oxides,  that 
which  contains  the  more  electro-negative  radicle  is  generally 
itself  electro-negative;  thus  sulphuric  acid  (regarded  as  SO3) 
is  electro-negative  to  all  metallic  oxides,  because  sulphur  is 
itself  electro-negative  to  all  metals:  on  the  other  hand  the 
oxides  of  potassium  and  sodium  are  electro-positive  to  all 
other  oxides  (excepting  those  of  caesium  and  rubidium)  be- 
cause potassium  and  sodium  are  themselves  electro-positive 
to  all  other  elements1  (except  caesium  and  rubidium). 

Polarity  and  chemical  affinity  are  closely  connected  in  the 
system  of  Berzelius:  the  'specific  unipolarity'2  however  does 
not  alone  determine  the  greater  or  less  affinity  of  one  atom 
for  another.  Some  atoms  have  a  more  intense  polarity  than 
others  and  therefore  exhibit  a  greater  striving  (Bestreben]  to 
neutralise  the  electricity  divided  between  their  poles,  in  other 
words,  have  a  greater  affinity  for  a  given  substance  than 
other  atoms. 

Chemical  affinity  appears  to  have  been  regarded  by  Ber- 
zelius as  nearly  synonymous  with  intensity  of  atomic  polarity3. 
Thus,  oxygen  combines  with  sulphur  rather  than  with  lead, 
although  oxygen  and  sulphur  have  the  same  unipolarity  (viz. 
negative);  but,  the  Berzelian  view  asserts,  the  positive  pole  of 
the  sulphur  atom  neutralises  more  negative  electricity  on  the 
oxygen  atom  than  can  be  neutralised  by  the  positive  pole  of 
the  lead  atom. 

1  An  important  deduction  made  from  these  considerations  is,  that  as  oxygen 
occurs  both  in  markedly  electro-positive  and  electro-negative  compounds,  and  as 
acids  are  as  a  group  electro-negative,  oxygen  cannot  be  the  acidifying  element,  as 
Lavoisier  said  it  was. 

2  Specifische  Unipolaritat.     Berzelius,  loc.  cit.  p.  73. 

3  This  might  perhaps  be  regarded  as  equivalent  to  the  modern  conception  of 
higher  and  lower  potential ;  as  if  one  atom  might  have  a  smaller  electrical  charge 
but  at  a  higher  potential  than  another,  and  would   therefore  exhibit  greater 
chemical  affinity  than  the  other. 


CH.  II.  §  48]  THE   DUALISTIC   THEORY.  115 

Double  decompositions  were  readily  explained  in  terms  of 
this  theory: 

"Every  chemical  action,"  says  Berzelius1,  "is  an  electrical  pheno- 
menon depending  on  the  electrical  polarity  of  the  particles ;  everything 
that  appears  to  be  due  to  the  action  of  affinity  is  caused  by  the  possession 
by  some  bodies  of  an  electrical  polarity  stronger  than  that  of  others.  If 
the  compound  AB  is  decomposed  by  the  substance  C  which  has  a  greater 
affinity  for  A  than  B  has,  then  C  must  possess  a  more  intense  electrical 
polarity  than  B ;  on  this  account  there  results  more  complete  neutralisa- 
tion between  A  and  C  than  between  A  and  B....  If  two  bodies,  AB  and 
CD,  so  react  as  to  produce  two  new  bodies,  AD  and  BC,  it  follows  that 
the  electrical  polarities  are  better  neutralised  in  the  latter  pair  of  bodies 
than  in  the  former." 

48  On  the  basis  of  this  conception  Berzelius  raised  the  struc- 
ture of  the  dualistic  chemistry,  which  asserted  that  every 
compound,  whether  simple  or  complex,  must  be  constituted  of 
two  parts,  of  which  one  is  positively,  and  the  other  negatively, 
electrified. 

The  doctrine  of  dualism  is  thus  introduced  by  Berzelius2: 
"  If  these  electro-chemical  conceptions  are  just,  it  follows  that  every 
chemical  compound  is  dependent  on  two  opposing  forces,  positive  and 
negative  electricity,  and  on  these  alone ;  and  that  every  compound  must 
be  composed  of  two  parts  held  together  by  their  mutual  electro-chemical 
reactions.  Therefore  it  follows  that  every  compound  body,  whatever  be 
the  number  of  its  constituents,  can  be  separated  into  two  parts,  whereof 
one  is  positively  and  the  other  negatively  electrified.  Thus,  for  example, 
sodium  sulphate  is  put  together,  not  from  sulphur,  oxygen,  and  sodium, 
but  from  sulphuric  acid  and  soda,  which  again  can  themselves  be  separated 
into  positive  and  negative  constituents.  So  also  alum  cannot  be  regarded 
as  immediately  built  up  from  its  elements,  but  must  rather  be  looked  on 
as  the  product  of  a  reaction  between  sulphate  of  alumina  and  sulphate  of 
potash,  the  former  acting  as  a  negative,  the  latter  as  a  positive  element."3 

In  support  of  his  theory  Berzelius  appealed  to  the  facts  of 
electrolysis.  A  solution  of  sodium  sulphate  containing  a  little 
blue  vegetable  colouring  matter  is  electrolysed ;  the  colouring 
matter  is  reddened  around  the  positive  electrode  and  rendered 

1  Lehrbuch  (ist  Ed.),  III.  part  I.  p.  77. 

8  Ibid.  p.  79. 

3  See  also  Berzelius,  Theorie  des  proportions  chimiques,  et  de  ^influence 
chimiqtie  de  V electricity  dans  la  nature  inorganique ;  3rd  Ed.  Paris,  1835.  Also, 
for  a  condensed  account  of  the  electro-chemical  theory  of  Berzelius,  see  Laden- 
burg,  Enhvickelutigsgcschichtc  dcr  Chemie,  pp.  89 — 93. 

8—2 


Il6  ATOMIC   AND   MOLECULAR   SYSTEMS.          [BOOK  I. 

more  distinctly  blue  around  the  negative.  What  can  this 
experiment  teach  but  that  the  salt  is  separated  by  the  electric 
current  into  alkali  and  acid  ?  And  can  the  inference  be 
avoided  that  the  salt  is  composed  of,  or  contains  in  itself, 
these  two  compound  radicles,  soda  (Na2O),  and  sulphuric 
acid  (SO3)?  All  salts  were  to  be  regarded  as  dualistic  struc- 
tures. Given  the  composition  of  a  salt,  a  dualistic  formula,  or 
rather  a  series  of  formulae,  was  at  once  devised  for  it.  The 
following  formulae  were  employed  by  various  dualistic  chemists 
to  express  the  structure  of  acetic  acid  : — 

(i)  C4H603.  H20  (2)  C4H604.  H2  (3)  C4H6O  .  O2.  H2O 

(4)  (C2H6)C203.H20  (5)  (C2H6)C204.H2  (6)  (C3H6O)CO2.  H2O 

(7)  C4H8 .  04  (8)  C2H4 .  02  (9)  C4H6O2 .  H2O2 
(10)  C4H2.04H6 

To  choose  the  proper  formula  from  such  a  chaos, was  a  task 
possible  only  for  one  whose  foible  was  omniscience.  That 
formula  which  had  the  weight  of  authority  on  its  side  was 
accepted  as  correct. 

49  Lavoisier  had  regarded  oxygen  as  the  '  acidifying  prin- 
ciple.' Hydrochloric  acid  was  undoubtedly  an  acid  sub- 
stance ;  therefore,  in  accordance  with  the  dictum  of  Lavoisier, 
it  contained  oxygen.  Davy's  study  of  this  compound,  and 
of  its  analogue  hydriodic  acid,  nevertheless  established  the 
fact  that  an  acid  can  exist  which  contains  no  oxygen.  The 
further  fact,  that  so  many  of  the  oxides — then  called  acids — 
exhibited  acidic  properties  only  in  presence  of  water,  led  Davy 
to  the  belief  that  very  many  acids  are  compounds  of  hydrogen. 
Shaking  off  the  trammels  of  that  older  philosophy  which  re- 
garded the  introduction  of  undefined  'principles'  as  affording 
explanations  of  natural  phenomena,  Davy  said  that  acids  are 
not  characterised  by  the  invariable  presence  of  any  one  ele- 
ment, but  that  certain  compounds  of  very  diverse  elements 
belong  to  this  group1. 

Dulong2  in   1815  further  advanced  Davy's  conception  of 
acids   by  recognising   no  essential  difference  between  those 

1  For  an  account  of  the  important  work  of  Davy  on  the  non-oxygenised  acids, 
and  the  arguments  of  his  opponents,  see  Ladenburg,  loc.  cit.  pp.  81 — 87. 

2  Mtm.  de  FAcad.  1813 — 15,  p.  198:  and  Schweigger's  Journal,  17.  229. 


CHAP.  II.  §§49 — 51]   THE  DUALISTIC  THEORY.  117 

acids  which  contain  oxygen  and  those  which  do  not. 
Lavoisier's  hypothesis  was  not  however  generally  abandoned 
until  many  years  later. 

In  1837 — 38  Liebig1,  following  up  Graham's  work  on 
phosphoric  acid2,  distinctly  recognised  the  existence  of  're- 
placeable hydrogen'  in  acids,  whether  oxy-acids  or  acids 
containing  no  oxygen,  and  defined  salts  to  be  compounds  be- 
longing to  the  same  class  as  acids,  and  formed  by  putting 
a  metal  in  the  place  of  an  equivalent  quantity  of  hydrogen  in 
acids3. 

This  view  of  the  structure  of  salts  was  altogether  opposed 
to  the  dualistic  theory  of  Berzelius. 

50  Another  severe  blow  was  inflicted  on  the  prevailing  theory 
by  Faraday's  researches  on  electrolytic  decompositions. 

Faraday  shewed  that  the  quantities  of  various  elements 
set  free  from  different  electrolytes,  by  the  same  electric 
current,  were  chemically  equivalent  to  one  another :  thus 
for  each  two  parts  by  weight  of  hydrogen  set  free  from 
water,  there  were  obtained  16  parts  of  oxygen,  78*2  parts 
of  potassium,  63-5  parts  of  copper  from  persalts  and  127 
parts  of  copper  from  protosalts.  But  the  affinities  of  the 
atoms  of  the  various  electrolytes  were  undoubtedly  different 
in  each  combination.  According  to  Berzelius,  the  quantity 
of  electricity  collected  on  any  group  of  atoms  is  greater,  the 
greater  the  mutual  affinity  of  these  atoms ;  but  Faraday's 
experiments  shewed,  that  in  so  far  as  this  electricity  was 
measurable  by  electrolytic  decomposition,  (and  that  at  least 
comparative  measurements  should  be  thus  obtained  followed 
from  the  terms  of  the  dualistic  theory  itself),  the  quantity 
of  it  was  in  no  way  dependent  on  the  affinities  of  the  com- 
bining atoms4. 

51  A  bold  and  partially  successful  attempt,  such  an  attempt 

1  Compt.  rend.  5.  863  (with  Dumas):   and  Annalen,  26.  113,  see  especially 
p.  181. 

2  Phil.  Trans,  for  1833.  253. 

3  See,    in   connexion   with   acid   generally,   Laurent,    Chemical  Method,  pp. 

39—45- 

4  See  Helmholtz,  'The  Faraday  Lecture.'     C.  S.  Journal,  Trans,  for  1881. 
pp.  284—6. 


Il8  ATOMIC   AND   MOLECULAR   SYSTEMS.          [BOOK  I. 

as  could  be  made  only  by  a  man  of  preeminent  power, 
had  been  made  by  Berzelius  to  found  chemical  classification 
on  the  study  of  composition  alone,  almost  wholly  divorced 
from  the  study  of  function  or  power  of  doing.  As  his  au- 
thority became  greater  Berzelius  led  chemistry  further  from 
the  only  true  path  by  which  she  could  advance,  that  namely 
wherein  experiment,  and  reasoning  on  experimental  data,  go 
hand  in  hand.  And  yet  no  single  chemist  has  enriched  the 
science  by  the  addition  of  so  great  a  mass  of  laboriously  and 
accurately  determined  experimental  data  as  he.  The  intense 
concentration  of  his  great  intellectual  powers  upon  one  view 
of  chemical  phenomena  led  Berzelius  to  disparage  the  reason- 
ing of  those  who  sought  to  view  these  phenomena  from  stand- 
points other  than  his  own. 

Among  those  who  recalled  chemistry  to  the  true  scientific 
method,  Dumas,  Laurent,  and  Gerhardt  stand  preeminent. 

In  I8391  Dumas  described  trichloracetic  acid,  obtained  by 
the  action  of  chlorine  on  acetic  acid.  The  new  compound, 
although  containing  chlorine  in  place  of  hydrogen,  was  a 
monobasic  acid  and  resembled  acetic  acid  in  its  general 
reactions.  Dumas  said  there  are  certain  types  in  organic 
chemistry  which  are  maintained  even  when  a  volume  of 
chlorine,  bromine,  or  iodine,  is  put  in  the  place  of  an  equal 
volume  of  hydrogen  in  the  parent  substance2. 

Berzelius,  and  the  defenders  of  the  dualistic  chemistry, 
violently  opposed  the  idea  that  the  electrically  negative 
chlorine  could  be  substituted  for  the  positive  hydrogen,  and 
the  identity  of  type  yet  be  maintained.  In  Dumas'  succeed- 
ing papers3  the  conception  of  types  was  more  fully  developed. 
All  compounds  composed  of  the  same  number  of  equivalents 
of  simple  substances,  combined  in  a  similar  manner,  and  ex- 
hibiting broad  analogies  of  properties,  were  regarded  as  be- 
longing to  the  same  type.  Such  compounds  were  also,  as  a 


1  Compt.  rend.  8.  609:  and  Annalen,  32.  101. 

2  Compt.  rend.  8.  621. 

3  Annalen,  33.  259:  35.  129  (with  Stas),  and  289  (with  Peligot) :  or  Compt. 
rend.  9.  813,  and  10.  149. 


CHAP.  II.  §52]  THE   UNITARY   THEORY.  119 

rule,  simply  related  to  one  another  by  reactions  of  formation 
and  decomposition  : — thus  acetic  and  chloracetic  acids  ;  chlo- 
roform, bromoform,  and  iodoform  ;  ethylene  and  its  chloro- 
derivatives,  &c.;  belonged  to  the  same  types,  or  as  Dumas 
said  to  the  same  'natural  families'.  Dumas  regarded  car- 
bonyl  chloride  as  derived  from  carbonic  anhydride  by  substi- 
tuting one  oxygen  by  two  chlorine  atoms ;  thus  COO  gives 
COC12 :  this  was  utterly  opposed  to  the  dualistic  view,  ac- 
cording to  which  the  formula  of  carbonyl  chloride  was 
written  CO .  CC14  because  every  compound  must  be  com- 
posed of  two  parts,  one  of  which  is  electrically  positive  and 
the  other  negative. 

52  The  new  school  of  chemists  naturally  opposed  the  con- 
ception of  compound  radicles,  a  conception  too  closely  asso- 
ciated with  those  dualistic  theories  they  were  leaving  behind 
to  find  favour  in  their  sight.  But  these  chemists  found  that, 
unless  substitution  of  simple  atoms  by  groups  of  atoms  were 
regarded  as  possible,  identity  of  type  could  not  be  maintained 
through  groups  of  compounds  undoubtedly  belonging  to  the 
same  natural  family. 

Inasmuch  as  the  new  chemistry  based  its  claims  to  re- 
cognition on  an  appeal  to  actual  reactions,  it  was  impossible 
that  it  should  long  refuse  to  recognise  the  conception  of 
compound,  as  well  as  simple,  radicles,  without  proving  false 
to  its  own  method.  Liebig  and  Wohler,  in  their  researches 
on  oil  of  bitter  almonds,  explained  the  observed  reactions 
of  the  bodies  they  obtained  by  assuming  the  existence  of 
the  compound  radicle  benzoyl  (=  CUH10O2)  in  these  bodies 
(see  Annalen,  3.  249). 

But  -what  are  these  compound  radicles  which  the  chemists 
who  upheld  the  unitary  system  were  obliged  to  recognise, 
equally  with  their  opponents  who  supported  a  dualistic  theory? 
Are  they  definite  groups  of  atoms  always  existing  as  such 
in  compound  molecules,  or  are  they  only  convenient  methods 
of  expressing  and  generalising  reactions  ? 

As  chemistry  advanced,  compound  radicles  came  to  be 
generally  recognised  as  certain  groups  of  atoms,  in  com- 
pound molecules,  which  remain  undecomposed  throughout 


120  ATOMIC   AND   MOLECULAR   SYSTEMS.          [BOOK  1 

a  series  of  reactions  undergone  by  those  molecules1.  Thus 
we  find  Kekule  in  1857  citing  the  case  of  sulphuric  acid, 
H2SO4,  which  when  acted  on  by  zinc  gives  ZnSO4,  and 
may  therefore  be  said  to  contain  the  radicle  SO4;  but  when 
acted  on  by  phosphorus  pentachloride,  the  compound  SO2C12 
is  produced,  hence  the  acid  may  be  said  to  contain  the 
radicle  SO.,. 

53        The  conception  of  types  was  destined  to  bear  much  fruit. 
Let  us  briefly  trace  its  development. 

Liebig  and  Dumas  had  regarded  salts  as  substituted 
metallic  derivatives  of  acids ;  they  had  spoken  of  a  quantity 
of  metal  as  taking  the  place  of  an  equivalent  quantity  of 
hydrogen :  Dumas  had  even  ventured  to  regard  the  negative 
chlorine  as  capable  of  replacing  an  equivalent  amount  of  the 
positive  hydrogen.  In  doing  this,  these  chemists  had  returned 
to  the  old  conception — too  much  forgotten  by  the  Berzelian 
school — of  equivalents  as  quantities  to  be  determined  by  the 
study  of  reactions  ;  but  they  had  given  this  conception  fresh  life 
by  engrafting  on  to  it  the  notion  of  natural  families  or  types. 

In  writing  the  formulae  of  sulphates,  selenates,  and  chro- 
mates,  as  MO .  SO3;  MO  .  SeO3;  and  MO  .  CrOs;  Berzelius  had 
undoubtedly  recognised  the  principle  of  types  ;  but  so  long  as 
this  principle  was  dominated  by  the  necessities  of  the  dual- 
istic  system  it  was  unfruitful.  The  idea  of  the  chemically 
reacting  unit  as  one  whole,  one  structure  with  parts  capable 
of  replacement  by  other  parts  without  the  necessary  de- 
struction of  the  building,  gave  meaning  to  what  was  before 
but  a  form  of  words. 

From  its  earliest  beginnings  to  its  present  form  the  theory 
of  types  has  been  interwoven  with  the  atomic  theory ;  with- 
out the  latter,  the  former  had  never  had  being.  If  the  value 
of  a  scientific  idea  is  to  be  measured  by  its  fruitfulness,  then 
is  Dalton's  New  System  of  Chemical  Philosophy  the  most  im- 
portant work  yet  produced  by  any  chemist. 

1  See  especially  Laurent's  Chemical  Method,  pp.  276 — 300  Also  Ladenburg, 
loc.  cit.  9th  and  roth  Lectures.  The  modern  development  of  the  conception  of 
compound  radicle  will  be  better  understood  by  considering  pars.  70—74  in 
Section  4  of  this  chapter. 


CHAP.  ii.  §53]  TYPES.  121 

Now  if  the  reacting  unit  of  any  substance  is  possessed 
of  a  definite  atomic  structure,  only  those  bodies  can  be  said 
to  belong  to  the  same  type,  or  natural  family,  whose  re- 
acting units  are  built  on  a  similar  atomic  plan  :  but  our 
only  method  of  discovering  similarity  of  structure  is  by  study- 
ing reactions  ;  hence  only  those  bodies  which  are  charac- 
terised by  similarity  of  chemical  function  ought  to  be 
classified  under  the  same  type1.  And  as  modification  of 
structure  has  been  recognised  as  not  necessarily  implying 
destruction  of  type,  it  follows  that  those  quantities  of  radi- 
cles, simple  or  compound,  are  equivalent,  which  can  perform 
similar  functions  in  similarly  constituted  compounds. 

At  last  a  method  of  chemical  classification  has  been  found 
by  Dumas,  Liebig,  Gerhardt,  and  Laurent,  which  when  more 
fully  developed  will  reconcile  those  who  regard  composition 
as  all  important,  with  those  for  whom  function  is  supreme ; 
which  will  preserve  the  fundamental  conception  of  equiva- 
lent, but  interpret  it  in  terms  of  the  wider  theory  of  atoms ; 
and  which  will  recognise  the  connexion,  while  yet  empha- 
sising the  importance  of  the  difference,  between  the  atom  of 
Dalton  and  the  molecule  of  Avogadro. 

But  in  its  development  the  theory  of  types  must  neces- 
sarily be  largely  modified.  Classification  by  types  cannot  be 
final  in  a  science  which  has  advanced  so  far  towards  be- 
coming an  abstract  science  as  chemistry. 

"  By  the  classification  of  any  series  of  objects  is  meant  the  actual,  or 
ideal,  arrangement  together  of  those  which  are  like  and  the  separation  of 
those  which  are  unlike ;  the  purpose  of  this  arrangement  being,  primarily, 
to  disclose  the  correlations  or  laws  of  union  of  properties  or  circumstances, 
and,  secondarily,  to  facilitate  the  operations  of  the  mind  in  clearly  con- 
ceiving and  retaining  in  the  memory  the  'character  of  the  objects  in 
question'."2 

Those  '  properties  or  circumstances '  which  are  correlated 
must  be  such  as  are  really  characteristic  of  the  objects  clas- 
sified, they  must  be  essential  properties  of  these  objects,  not 
mere  surface  appearances ;  they  must  be  capable  of  accurate 

1  See  especially  Laurent's  Chemical  Method,  pp.  298 — 300. 

2  W.  Stanley  Jevons  (modifying  the  words  of  Huxley),  Principles  of  Science, 
2.  p.  348. 


122  ATOMIC   AND    MOLECULAR   SYSTEMS.          [BOOK  I. 

definition,  and  at  the  same  time  of  fairly  easy  recognition  ; 
and  that  property,  or  properties,  chosen  as  the  mark  of 
a  class  must  belong  to  all  the  members  of  that  class. 

But  the  properties  of  a  type  are  necessarily  somewhat 
vague:  properties  regarded  by  one  observer  as  essentially 
belonging  to  the  type  may  by  another  be  regarded  as  acci- 
dental;  a  given  substance  may  possess  so  many  of  the 
properties  of  the  type  as  at  one  time  suffices  to  ensure  its 
admission  into  the  class,  but  at  a  future  time  new  proper- 
ties may  be  discovered  which  necessitate  the  removal  of  the 
substance  to  a  class  whose  type  shews  considerable  diver- 
gence from  that  under  which  the  substance  was  originally 
placed. 

The  very  elasticity,  and  even  vagueness,  of  the  theory 
of  types  ensured  it  an  important  place  in  the  development 
of  chemical  science. 


SECTION  III.     Equivalency  of  atoms, 

54  Dualism  had  reigned  supreme,  but  only  because  it  was 
despotic;  when  the  rebellion,  headed  by  Dumas,  once  got  a 
footing  the  fate  of  the  older  theory  was  sealed.  The  new 
system  succeeded  because  it  was  not  too  systematic. 

In  attempting  to  preserve  unity  of  type  through  large 
series  of  compounds,  the  builders  of  modern  chemistry  were 
obliged  to  make  free  use  of  the  conception  of  compound 
radicles  as  substituting  simple  radicles ;  they  thus  became 
familiarised  with  the  general  notion  of  each  radicle  pos- 
sessing a  definite  substituting  power. 

In  1852  Frankland1  extended  this  conception  to  the 
atoms  of  the  elementary  bodies;  in  1855  Odling2  introduced 
the  use  of  dashes  placed  over  the  atomic  symbols  to  express 
what  he  called  '  the  replaceable,  or  representative,  or  substitu- 

1  Phil.  Trans.  142.  417,  see  especially  p.  440. 

2  C.  S.  Journal,  1.  i .     (The  recognition  of  two  '  replaceable  values '  for  the 
iron  atom,  and  other  atoms,  shews  the  close  connexion  between  the  theory  then 
coming  into  existence  and  the  older  theory  of  equivalents.) 


CHAP.  II.  §54]  EQUIVALENCY   OF   ATOMS.  12$ 

tion  value '  of  these  atoms,  he  also  recognised  that  an  ele- 
mentary atom  may  have  more  than  one  'replaceable  value'. 
Odling  applied  this  fruitful  conception  to  the  formulae  of 
many  salts,  especially  the  phosphates,  and  succeeded  in 
shewing  analogies  until  then  overlooked. 

The  inherent  fascination  of  the  idea  of  the  compound 
radicle  may  be  realised,  by  considering  that  in  less  than 
twenty  years  after  Dumas'  discovery  of  the  chloracetic  acids, 
a  discovery  which  marks  the  beginning  of  the  revolt  against 
the  compound  radicles  of  dualism,  Kekule1,  and  inde- 
pendently of  him  Couper2,  (in  papers  of  the  greatest  im- 
portance) found  it  necessary  to  recall  chemists  to  the  con- 
sideration of  elementary  atoms  as  being  the  true  units  by  the 
combinations  of  which  all  compound  molecules  are  built  up, 
and  by  whose  properties  those  of  the  compounds  are  deter- 
mined. Couper  criticised  Gerhardt's  development  of  types, 
objecting  to  the  vagueness  of  the  idea  as  a  basis  for  classifi- 
cation ;  and  especially  opposing  Gerhardt's  opinion  that  the 
molecular  constitution  of  bodies  can  never  be  ascertained  by 
chemists.  "  Would  it  not  be  rational,"  says  Couper,  "  in  ac- 
cepting this  veto  to  renounce  chemical  research  altogether?" 
This  dictum  of  Gerhardt  is  to  be  traced,  in  Couper's  opinion, 
to  the  overdue  employment  of  compound  radicles,  to  for- 
getting that  these  can  have  no  properties  which  are  not 
"a  direct  consequence  of  the  properties  of  the  individual 
elements  of  which  they  are  made  up,"  and  hence  to  endow- 
ing these  radicles  with  some  "  unknown  and  ultimate  power 
which  it  is  impossible  to  explain."  Returning  then  to  a 
study  of  the  elements,  Couper  finds  chemical  affinity  as  a  pro- 
perty inherent  in,  and  common  to,  them  all ;  he  distinguishes 
'  affinity  of  kind '  and  '  affinity  of  degree ;'  applying  the  latter 
to  carbon,  he  cites  the  oxides  CO  and  CO2  (in  his  notation 
C2O2  and  C2OJ,  the  former  expressing  the  first,  the  latter  the 
second  and  last,  degree:  CO2  is  "the  ultimate  affinity,  or 
combining  unit,  for  carbon." 

Kekule  in  1857,  and  more  especially  in  a  paper  published 

1  Annalen  (1857),  104.  129. 

2  Phil.  Mag.  (1858)  [4],  16.  104. 


124  ATOMIC   AND   MOLECULAR   SYSTEMS.  [BOOK  I. 

in  March  1858*,  a  paper  the  importance  of  which  can  hardly 
be  overrated,  distinguishes  more  clearly  than  Couper  'affi- 
nity of  kind'  from  'affinity  of  degree';  or  rather  he  distin- 
guishes chemical  affinity  from  what  he  calls  the  'basicity  of 
atoms';  both  conceptions  being  needed,  he  says,  for  the 
explanation  of  chemical  combinations.  Kekule  clearly  dis- 
tinguishes, and  this  distinction  has  been  too  much  forgotten 
in  recent  developments  of  chemical  theory,  between  equi- 
valent weights  of  elements,  and  equivalency  (or  basicity)  of 
elementary  atoms;  he  shews  that  the  new  theory  deals 
with  definite  entities,  called  atoms,  having  defined  properties, 
and  not  with  'unit  weights,'  and  that  it  is  these  atoms  which 
he  proposes  to  compare  as  to  their  substituting  power  for  the 
.hydrogen  atom.  Having  shewn  that  one  atom  of  carbon, 
so  far  as  our  knowledge  goes,  is  never  combined  with  more 
than  four  atoms  of  hydrogen  in  a  compound  molecule,  Kekule 
also  shews  that  two  atoms  of  carbon  do  not  bind  to  them- 
selves more  than  six  atoms  of  hydrogen,  three  atoms  of 
carbon  not  more  than  eight  atoms  of  hydrogen,  and  so  on. 

The  tetravalency  of  the  carbon  atom,  and  the  power 
which  two,  or  more,  atoms  of  carbon  possess  of  binding  them- 
selves together  in  a  molecule,  are  enunciated  by  Kekule  in 
this  paper,  which  forms  the  foundation  stone  of  the  modern 
hypothesis  of 'atom-linking.'2 

Kekule  and  Couper  insisted,  that  if  a  definite  conception  of 
the  connexions  between  the  properties  and  the  structure  of 
compounds  is  to  be  obtained,  it  must  be  based  on  the  study 
of  the  combining  powers  of  the  elementary  atoms:  'The 
whole  is  simply  a  derivative  of  its  parts,'  said  Couper. 
55  An  hypothesis  which  shall  attempt  to  explain  the  atomic 
structure  of  compound  molecules,  must,  in  the  present  state 
of  knowledge,  be  based  on  the  consideration  of  gaseous 
bodies.  We  do  not  know  how  to  determine  the  relative 

1  Annalen,  106.  129. 

2  In  comparing  Couper's  paper  with  Kekule's  it  may  be  well  to  notice  how 
Couper  attempts  to  trace  a  close  connexion  between  the  basicity  of  atoms  and 
chemical  affinity;  his  statements  are  here  much  vaguer  than  Kekule's,  yet  this 
dynamical  method  of  regarding  'valency'  at   the  very  outset  of  the  theory  is 
important. 


CHAP.  II.  §§55,  56]       VALENCY   OF   ATOMS.  125 

weights  of  the  molecules  of  solid  or  liquid  substances ;  indeed 
the  term  molecule  is  used  with  a  strictly  definite  meaning 
only  when  applied  to  gases.  We  have  reason  to  believe  that 
the  ultimate  structure  of  a  mass  of  a  solid  or  liquid  is  much 
more  complex  than  that  of  a  mass  of  a  gaseous  substance; 
no  generalisations  have  yet  been  made  regarding  the  mo- 
lecular phenomena  of  solids  or  liquids  comparable  with  those 
which — under  the  names  of  the  laws  of  Boyle,  Charles,  and 
Avogadro — have  been  made  regarding  the  molecular  phe- 
nomena of  gases.  We  must  recognise  the  limits  within  which 
an  hypothesis  regarding  atomic  structure  can  assist  advance; 
if  it  be  pushed  too  far  it  will  become,  with  some  a  dogma, 
with  others  a  thing  to  be  scorned. 

Consider  these  four  molecular  formulae  HC1,  H2O,  H3N, 
H4Si.  It  is  seen  that  one  atom  of  chlorine  is  combined  with 
one  atom  of  hydrogen  in  the  molecule  HC1,  that  one  atom  of 
oxygen  is  combined  with  two  atoms  of  hydrogen  in  the  mole- 
cule H2O,  that  one  atom  of  nitrogen  is  combined  with  three 
atoms  of  hydrogen  in  the  molecule  H3N,  and  that  one  atom 
of  silicon  is  combined  with  four  atoms  of  hydrogen  in  the 
molecule  H4Si.  Considering  the  molecular  formulae  C1H, 
Cl2Hg,  Cl3Bi,  and  Cl4Sn,  it  is  seen  that  one  atom  of  hydrogen 
is  comb'ned  with  one  atom  of  chlorine,  one  atom  of  mercury 
with  two  atoms  of  chlorine,  one  atom  of  bismuth  with  three 
atoms  of  chlorine,  and  one  atom  of  tin  with  four  atoms  of 
chlorine,  in  these  compound  molecules. 

These  facts  may  be  expressed  by  saying  that  the  atoms  of 
oxygen  and  mercury  are  divalent,  the  atoms  of  nitrogen  and 
bismuth  are  trivalent,  and  the  atoms  of  silicon  and  tin  are 
tetravalent;  i.e.  so  far  as  the  data  at  present  before  us  are  con- 
cerned, the  atom  of  oxygen,  and  that  of  mercury,  combines 
with  two  atoms  of  hydrogen  or  of  chlorine ;  the  atom  of 
nitrogen,  and  that  of  bismuth,  combines  with  three  atoms  of 
hydrogen  or  of  chlorine;  the  atom  of  silicon,  and  that  of  tin, 
combines  with  four  atoms  of  hydrogen  or  of  chlorine,  to 
form  compound  molecules. 

56        But  these  terms  monovalent,  divalent,  &c.,  atoms  must  be 
more  strictly  defined. 


126  ATOMIC   AND   MOLECULAR   SYSTEMS.          [BOOK  I. 

Let  us  begin  by  attempting  to  define  the  expression,  a 
monovalent  atom.  Let  those  atoms  which  combine  each  with 
one,  and  not  more  than  one,  atom  of  hydrogen  to  form 
gaseous  molecules,  be  placed  together  and  called  monovalent 
atoms.  Then  the  atoms  of  hydrogen,  chlorine,  bromine,  iodine, 
and  probably  fluorine,  are  monovalent ;  the  evidence  is  the 
existence  of  the  gaseous  molecules  HH,  HC1,  HBr,  HI,  and 
HF1,  and  the  non-existence  of  any  gaseous  molecules  com- 
posed of  a  single  atom  of  hydrogen,  chlorine,  bromine,  iodine 
(or  ?  fluorine),  and  more  than  one  atom  of  hydrogen.  The 
term  monovalent  strictly  implies  that  all  the  atoms  to  which 
it  is  applied  are  equivalent,  or  of  equal  value  in  exchange. 
It  is  important  to  observe  that  as  regards  combination  with 
one  atom  of  hydrogen  to  produce  gaseous  molecules,  the 
atoms  of  chlorine,  bromine,  iodine,  and  probably  fluorine, 
are  equivalent ;  but  that  it  is  quite  possible  that  these  atoms 
may  not  be  equivalent,  or  of  equal  value  in  exchange,  in 
other  respects. 

If  it  is  assumed  that  an  atom  which  combines  with  not 
more  than  two  atoms  of  chlorine,  bromine,  iodine,  or  fluorine, 
is  equivalent  to  another  atom  which  combines  with  not  more 
than  two  atoms  of  hydrogen,  then  we  arrive  at  the  definition 
of  a  divalent  atom  as  an  atom  which  combines  with  not  more 
than  two  monovalent  atoms  (i.e.  atoms  of  hydrogen,  chlorine, 
bromine,  iodine  or  fluorine)  to  form  gaseous  molecules.  Simi- 
larly, definitions  of  trivalent,  'tetravaleut,  &c.  atoms  are  found. 
Applying  these  definitions  to  the  data  contained  in  the  table 
on  pp.  39 — 43  we  arrive  at  the  following  classification  of 
atoms. 

1  Mallet  [Amer.  Chem.  Journal  3.  189]  has  shewn  that  at  low  temperatures 
the  molecule  of  hydrofluoric  acid  must  be  represented  by  the  formula  H2F2;  at 
higher  temperatures  however  the  formula  HF  represents  the  molecule  of  this 
gas.  It  is  possible  that  hydrofluoric  acid  is  a  'molecular  compound'  at  low 
temperatures  (see  Section  5  of  the  present  chapter) :  determinations  of  the  spec, 
gravity  of  this  gas  for  a  considerable  range  of  temperature  and  pressure  would 
throw  light  on  this  question. 


CHAP.  II.  §56]  VALENCY   OF   ATOMS.  127 


STANDARD  MONOVALENT  ATOMS;  H,  F,  Cl,  Br,  I. 

I.  Monovalent  atoms ;  i.e. 

atoms  which  combine  with  one  standard  monovalent  atom  to  form 
gaseous  molecules  ... K,  Rb,  Ag,  Cs,  Hg,  Tl. 

II.  Di i <alen t  atoms ;  i.e. 

atoms  which  combine  with  two  standard  monovalent  atoms  to  form 
gaseous  molecules    O,  S,  Se,  Te,  Be,  Cd,  Zn,  Hg,  Sn,  Pb,  Mn. 

III.  Trivalent  a toms ;  i.e. 

atoms  which  combine  with  three  standard  monovalent  atoms  to  form 
gaseous  molecules    B,  N,  Al,  P,  Cr,  As,  Sb,  Bi,  In. 

IV.  Tetravalcnt  atoms  ;  i.e. 

atoms  which  combine  with  four  standard  monovalent  atoms  to  form 
gaseous  molecules. ..C,  Si,  Ti,  Ge,  Zr,  V,  Sn,  Te,  Th,  U,  Pb  (s.  p.  128). 

V.  Pentavalent  atoms ;  i.e. 

atoms  which  combine  with  Jive  standard  monovalent  atoms  to  form 
gaseous  molecules P,  Nb,  Ta,  Mo,  W. 

VI.  Hexavalent  atoms ;  i.e. 

atoms  which  combine  with  six  standard  monovalent  atoms  to  form 
gaseous  molecules W. 

The  data  on  which  this  classification  of  atoms  rests  are 
presented  in  the  following  list  of  formula::  which  shew  the 
compositions  of  all  gaseous  molecules  composed  of  one  of 
the  standard  monovalent  atoms  combined  with  a  single  atom 
of  any  other  element : — 

KI,  RbCl,  Rbl,  AgCl,  CsCl,  Csl,  HgCl,  T1C1 ;  BeCl2, 
BeBr2,  OH8,  OC12>  SH2,  MnCl2,  SeHs,  TeH2,  TeCl2,  CdBr2, 
ZnCl2,  HgCl2,  HgBr2,  HgI2,  SnCl2,  PbCl2;  BF3,  BC13,  BBr3, 
NH3,  A1C13,  PH3,  PC13,  CrCl3,  AsH3,  AsCl3,  AsI3,  SbCl3, 
SbI3,  BiCl3,  InCl3;  CH4,  CC14,  SiF4,  SiCl4,  SiI4,  GeCl4,  GeI4, 
TiCl4,  ZrCl4,  VC14,  SnCl4,  SnBr4,  TeCl4,  ThCl4,  UBr4,  UC14; 
PF5,  NbCl5,  TaCl5,  MoCl8,  WC16;  WC18. 

When  it  is  said  that  one  atom  is  combined  with  a  certain 
number  of  standard  monovalent  atoms,  direct  interaction 
between  these  atoms  in  the  molecule  is  assumed.  Thus  the 
statement  that  one  atom  of  bismuth  is  combined  with  three 


128  ATOMIC  AND   MOLECULAR   SYSTEMS.          [BOOK  I. 

monovalent  atoms  of  chlorine  in  the  gaseous  molecule  BiCl3 
implies,  that  in  this  molecule  there  is  direct  action  and 
reaction  of  some  kind  between  the  atom  of  bismuth  and 
each  of  the  atoms  of  chlorine.  It  might  be  that  the  atom 
of  bismuth  interacts  directly  with  one,  or  two,  atoms  of 
chlorine  and  only  indirectly  with  the  other  atoms ;  but  con- 
sidering that  one  atom  of  chlorine  is  never  found  combined 
with  more  than  a  single  atom  of  hydrogen,  bromine,  or  iodine, 
in  gaseous  molecules  composed  of  any  two  of  these  elements, 
considering,  that  is  to  say,  that  the  atom  of  chlorine  is  by 
definition  monovalent,  the  simplest  hypothesis  is  that  the 
atom  of  bismuth  interacts  directly  with  each  of  the  chlorine 
atoms  in  the  gaseous  molecule  BiCls,  in  other  words,  that  the 
atom  of  bismuth  is  trivalent  in  this  molecule. 

The  groups  of  atoms,  methyl  CH8,  and  ethyl  C2H5,  may 
be  regarded  as  monovalent,  inasmuch  as  each  combines 
with  one  and  not  more  than  one  of  the  standard  monovalent 
atoms  to  form  gaseous  molecules1.  If  the  formulae  of  those 
gaseous  molecules  which  are  composed  of  a  single  atom  of 
an  element  combined  with  one  of  the  groups  of  atoms  methyl 
or  ethyl  are  tabulated,  we  find  that  the  atom  of  lead  is  tetra- 
valent  as  well  as  divalent2. 

The  table  on  p.  127  contains  37  elements  (besides  the 
five  standard  monovalent  elements);  the  atoms  of  six  of  these 
are  found  each  in  two  classes.  The  atom  of  mercury  is 
monovalent  and  divalent,  the  atoms  of  tellurium,  tin,  and 
lead  are  divalent  and  tetravalent,  the  atom  of  phosphorus 
is  trivalent  and  pentavalent,  and  the  atom  of  tungsten  is 
pentavalent  and  hexavalent.  This  variation  in  the  valency  of 
certain  atoms  is  not  surprising  when  we  recall  the  fact  that 
an  element  has  frequently  more  than  one  equivalent  weight, 
and  we  consider  that  the  object  of  the  classification  of  atoms 
in  accordance  with  their  valencies  is  to  place  together  those 
atoms  which  are  equivalent,  that  is  of  equal  value  in  exchange. 

1  These  molecules  are  (CH3)H,  (CH^F,  (CH3)C1,  (CH3)Br,  (CH3)I,  (C2H8)H, 
(C2H6)C1,  (C2H6)Br,  (C2H5)L 

2  The  molecules  in  question  are  these;— Hg(CH3)2,  Hg(C2H5)2,  Zn(CH3)2, 
B(CH:))3,  Sh(C2H5)3,  Si(C2H5)4,  Sn(C2H5)4,  Pb(CH3)4. 


CHAP.  II.  §5 7]  VALENCY  OF  ATOMS.  1 29 

57  We  have  now  gained  definitions  of  the  terms  monovalent, 
divalent,  trivalent,  &c.  as  applied  to  atoms.  The  atoms  of 
hydrogen,  chlorine,  bromine,  iodine,  (and  fluorine)  are  equi- 
valent in  this  respect  that  each  combines  with  one  and 
only  one  atom  of  hydrogen  to  form  gaseous  molecules ; 
these  atoms  are  therefore  taken  as  the  standard  mono- 
valent atoms. 

The  valency  of  any  other  atom  is  determined  by  finding 
the  number  of  standard  monovalent  atoms  with  which  it 
combines  to  form  gaseous  molecules,  the  maximum  valency 
being  measured  by  the  maximum  number  of  these  standard 
monovalent  atoms.  It  is  certain  that  some  atoms  com- 
bine now  with  one  number,  and  now  with  another  number, 
of  standard  monovalent  atoms,  to  form  gaseous  mole- 
cules. 

The  valency  of  the  atom  of  an  element  cannot  be  accu- 
rately determined  except  at  least  one  gasifiable  compound 
has  been  obtained  composed  of  a  single  atom  of  the  element 
in  question  combined  with  standard  monovalent  atoms,  and 
with  such  atoms  only.  Thus  the  valencies  of  the  atoms 
of  aluminium,  iron,  copper,  and  gallium  cannot  be  defi- 
nitely determined  from  considering  the  compositions  of  the 
following  gaseous  molecules ; — Al2Brd,  A12I6,  Fe2Cl6,  Cu8Cl2, 
Ga2Cl, 

We  might  now  define  the  valency  of  an  atom  to  be  the 
maximum  number  of  atoms  of  hydrogen,  fluorine,  chlorine, 
bromine,  or  iodine,  with  which  the  specified  atom  combines 
to  form  gaseous  molecules  ;  but  when  we  apply  this  definition 
we  find  it  too  limited.  An  examination  of  the  composi- 
tions of  the  gaseous  molecules  tabulated  on  p.  127  leads  to 
the  notion  of  a  limit  to  the  number  of  atoms  between  which 
direct  interaction  occurs  in  gaseous  molecules.  This  con- 
ception may  be  put  into  a  definite  form  of  words,  thus ;  each 
atom  in  a  gaseous  molecule  can  directly  interact  with  a 
limited  number  of  other  atoms.  From  this  conception  the 
definition  of  valency  easily  follows :  the  valency  of  an  atom 
is  a  number  which  expresses  the  maximum  mimber  of  oilier 
atoms  between  which  and  the  specified  atom  tiiere  is  direct  inter- 
M.  c.  9 


130  ATOMIC  AND   MOLECULAR   SYSTEMS.          [BOOK  I. 

action  in  any  gaseous  molecule.  This  definition  furnishes  an 
excellent  working  hypothesis  in  all  attempts  to  learn  anything 
of  the  arrangement  of  the  parts  of  molecules. 

But  while  the  definition  of  valency  of  an  atom  is  widened, 
we  must,  I  think,  always  determine  the  valency  of  any 
specified  atom  by  considering  the  compositions  of  gaseous 
molecules  composed  only  of  that  atom  and  the  standard 
monovalent  atoms,  hydrogen,  fluorine,  chlorine,  bromine, 
and  iodine.  If  a  specified  atom  combines  with  not  more 
than  n  standard  monovalent  atoms,  then  we  conclude  that 
this  atom  will  not  directly  interact  in  any  gaseous  molecule 
with  more  than  n  atoms  of  any  element.  The  greater  the 
number  of  gaseous  molecules  composed  of  the  specified  atom 
and  atoms  of  hydrogen,  fluorine,  &c.  which  have  been  ex- 
amined, the  greater  is  the  probability  that  the  value  of  ;/ 
expresses  the  true  maximum  valency  of  the  atom  in  question. 
Thus,  suppose  that  the  gaseous  molecules  SnCl4  and  SnBr4 
were  unknown,  the  existence  of  the  molecule  SnCl2  would 
lead  us  to  place  the  atom  of  tin  in  the  class  of  divalent 
atoms. 

As  only  six  of  the  37  atoms  whose  valencies  have  been 
accurately  determined  (excluding  the  standard  monovalent 
atoms)  shew  variations  of  valency,  we  may  provisionally  re- 
gard the  value  found  for  the  valency  of  an  atom  from  the 
composition  of  even  a  single  molecule  composed  of  that 
atom  and  any  of  the  standard  monovalent  atoms  as  the 
true  valency  of  the  specified  atom.  At  any  rate  we  must 
make  use  of  this  value  in  all  discussions  regarding  the 
arrangement  of  the  parts  of  molecules  into  which  this  atom 
enters  so  long  as  no  direct  proof  is  forthcoming  that  the 
value  is  erroneous;  and  the  only  direct  proof  is  the  forma- 
tion and  analysis  of  gaseous  molecules  composed  of  the 
specified  atom  and  a  number  of  standard  monovalent  atoms 
different  from  the  number  present  in  the  gaseous  molecule 
on  the  composition  of  which  the  value  originally  adopted 
for  the  valency  of  the  atom  in  question  was  based.  If  we 
allow  ourselves  to  vary  the  valencies  of  atoms  without 
cogent  proof  endless  confusion  arises,  and  the  applications 


CHAP.  II.  §§57— 59]  VALENCY   OF   ATOMS.  131 

of  the  hypothesis  of  valency  become  merely  amusing  exer- 
cises of  fancy. 

When  therefore  it  is  said  in  this  book  that  the  atom  of 
a  certain  element  is  n  valent,  the  statement  is  to  be  un- 
derstood as  asserting,  (i)  that  one  or  more  gaseous  molecules 
are  known  composed  of  a  single  atom  of  the  specified  element 
combined  with  n  atoms  of  hydrogen,  fluorine,  chlorine,  bro- 
mine, or  iodine ;  (2)  that  no  gaseous  molecule  is  known 
composed  of  a  single  atom  of  the  specified  element  and 
more  than  n  atoms  of  hydrogen,  fluorine,  &c. ;  and  (3)  that 
in  discussions  regarding  the  arrangement  of  the  parts  of 
molecules  of  which  the  specified  atom  forms  a  constituent, 
we  shall  assume  that  direct  interaction  occurs  between  the 
specified  atom  and  not  more  than  n  other  atoms  of  any  kind. 
58  Such  a  statement  as  '  the  atom  of  phosphorus  is  trivalent 
in  the  molecule  PC13,'  or  '  the  atom  of  carbon  is  trivalent  in 
the  molecule  C2H4,'  asserts  that  the  atom  named  directly 
interacts  in  the  specified  molecule  with  three  other  atoms; 
such  statements  do  not  assert  that  the  maximum  valency 
of  the  specified  atom  is  defined  by  its  actual  valency  in  the 
particular  molecule  referred  to.  Such  a  statement  as  '  the 
atom  of  arsenic  is  trivalent'  implies  that  the  maximum 
valency  of  this  atom  is  three. 

9  The  atoms  of  hydrogen,  fluorine,  chlorine,  bromine,  and 
iodine  were  placed  in  one  class  and  said  to  be  equivalent, 
because  each  combines  with  a  single  atom  of  hydrogen  to 
form  gaseous  molecules.  The  atoms  of  37  other  elements 
were  then  arranged  in  classes,  and  the  members  of  each  class 
were  said  to  be  equivalent  because  they  all  combine  with 
the  same  number  of  atoms  of  hydrogen,  or  fluorine,  or 
chlorine,  or  bromine,  or  iodine,  to  form  gaseous  molecules. 
The  conception  of  equivalency  has  evidently  been  widened  ; 
an  atom  of  hydrogen  is  regarded  as  equivalent  to  an  atom 
of  chlorine  not  only  as  regards  the  combination  of  each  with 
hydrogen  atoms,  but  also  as  regards  the  combination  of 
each  with  certain  other  atoms.  Then  the  notion  of  equiva- 
lency was  yet  further  widened,  and  it  was  said  that  all  atoms 
which  are  equivalent  in  respect  that  they  combine  with  « 

9—2 


132  ATOMIC   AND   MOLECULAR   SYSTEMS.          [BOOK  I. 

atoms  of  hydrogen,  fluorine  &c.  are  also  equivalent  in  respect 
that  they  directly  interact  with  n  atoms  of  any  kind  in 
gaseous  molecules.  The  words  equivalent  to  have  been  used 
with  an  ever  widening  meaning.  It  might  be,  and  it  has 
very  often  been,  urged  that  to  say  that  an  atom  is  divalent 
is  the  same  thing  as  to  say  that  the  atom  is  equivalent  to 
two  monovalent  atoms.  Thus,  to  say  that  the  atom  of  oxygen 
is  divalent,  it  may  be  argued,  is  an  assertion  that  one  atom 
of  oxygen  is  equivalent  to  two  atoms  of  hydrogen,  fluorine, 
&c.  If  we  are  careful  to  recall  the  exact  meaning  of  the 
words  equivalent  to  in  this  statement,  then,  it  seems  to  me, 
that  no  valid  objection  can  be  brought  against  the  statement. 
Now  the  words  equivalent  to  here  mean,  combines  with  the 
same  number  of  standard  monovalent  atoms  as;  no  other 
kind  of  equivalency  between  one  atom  of  oxygen  and  two 
atoms  of  hydrogen,  &c.  is  asserted.  But  the  limitation  of 
the  meaning  of  the  term  equivalent  in  connexion  with  the 
valencies  of  atoms  has  been  too  much  forgotten.  Thus,  it 
has  been  argued  that  because  an  atom  of  oxygen  is  divalent, 
and  because  the  gaseous  molecules  CO  and  CO2  exist,  there- 
fore the  atom  of  carbon  is  divalent  in  the  molecule  CO  and 
tetravalent  in  the  molecule  CO2.  To  say  this  appears  to 
me  to  be  using  a  phrase  which  has  no  accurate  meaning. 
60  As  there  has  been  much  discussion  regarding  such  phrases 
as  this,  it  behoves  us  to  consider  some  of  them  more  closely. 
The  valency  of  an  atom  is  generally  expressed  by  a  Roman 
numeral  placed  over  the  symbol  of  the  element,  thus  CIV,  P111 ; 

or  by  lines  proceeding  from  the  symbol,  thus  — C-,  — P— . 

i  i 

It  required  but  a  short  time  from  the  introduction  of  this 
notation  for  chemists  to  forget  that  these  lines  are  only  a 
form  of  language.  From  speaking  of  the  valency  of  an  atom, 
they  soon  came  to  speak  of  each  line  as  a  valency,  or  a  unit 
of  affinity,  and  to  assert  that  such  or  such  an  atom  has  four 
(or  three  or  two  &c.)  units  of  affinity  or  valencies.  Then 
they  went  a  step  farther,  and  asserted  that  in  the  molecule 
CO  two  of  the  four  valencies  or  units  of  affinity  of  the 
tetravalent  carbon  atom  are  satisfied  by  the  two  valencies 


CHAP. ii. §§60,61]     USE  OF 'BONDS' OR 'LINKS.'  133 

of  the  divalent  oxygen  atom,  and  that  in  the  molecule  CO2 
all  the  affinities  of  the  carbon  atom  are  satisfied  by  the  four 
valencies  of  the  two  oxygen  atoms.  These  assertions  were 
embodied  in  the  symbols  C  =  O  and  O  =  C  =  O.  Similarly, 
the^  symbols  H2  =  C  =  C  =  H2  and  H  —  C  =  C  —  H  were  used 
to  represent  the  distributions  of  the  units  of  affinity,  or  the 
valencies,  of  the  atoms  of  carbon  and  hydrogen  in  the  mole- 
cules C2H4  and  C2H2.  Then  such  phrases  as  '-carbon  atoms 
linked  by  double  and  treble  bonds '  and  '  doubly  and  singly 
linked  carbon  atoms '  were  employed. 
61  What  definite  meanings  can  be  given  to  such  expressions 
and  such  symbols  ? 

(1)  The  statement1   that  an    atom  of  carbon  has  four 
valencies  or  four  units  of  affinity  cannot  mean  that  the  force 
of  affinity  of  a  carbon  atom  is  divided  into  four  parts  within 
that  atom,  for  'force'  has  no  meaning  apart  from  two  or 
more  reacting  bodies :  force  is  a  name  given  by  one  of  the 
parties  to  a  transaction,  but  a  transaction  involves  at  least 
two  transacting  parties.     The  force  between  a  carbon  atom 
and  another  atom  must  vary  with  external  conditions,  prob- 
ably with  the  distance,  the  mass,  and  the  chemical  nature, 
(a  vague  term  but  perhaps  as  good  as  can  be  given  at  present) 
of  both  atoms. 

(2)  The  carbon  atom  has  four  equivalencies,  or  four  units 
of  affinity.     This  cannot  mean  that  four  parts  of  the  carbon 
atom  are  chemically  active,  and  the  other  parts  inactive :  such 
a  hypothesis  leads  at  present  to  contradictions  (see  appendix 
to  Section  4);  moreover  in  the  present  state  of  knowledge  it 
is  inadvisable  to  hazard  hypotheses  as  to  the  inner  structure 
of  atoms  in  order  to  explain  chemical  phenomena.     Atoms 
may  not  be  homogeneous,  but  at  present  they  are  the  ulti- 
mate particles  to  be  considered  in  chemical  changes. 

(3)  The   expression    under   consideration   cannot   mean 
that  the  chemical  energy  of  a  carbon  atom  is  divided,  or  js 

1  A  paper  of  the  greatest  importance  entitled  '  Ueber  die  Vertheilung  der 
Atome  in  der  Molekel,'  by  W.  Lessen,  appeared  in  Annalen,  204.  265.  I  have 
made  free  use  of  this  paper  in  the  present  chapter.  (See  also  Claus,  Ber.  14. 
432  ;  and  Lessen,  ibid.  760.) 


134  ATOMIC   AND   MOLECULAR   SYSTEMS.         [BOOK  I. 

always  divisible,  into  four  parts.  What  is  to  be  the  unit  of 
chemical  work  ?  the  mass  of  matter  fixed  by  a  given  atom  ? 
where  then  is  the  equivalency  between  one  atom  of  oxygen 
with  the  mass  1 6  and  two  atoms  of  chlorine  with  the  mass  7 1  ? 
Let  a  carbon  atom  combine  with  four  hydrogen  atoms,  the 
total  chemical  energy  of  the  atoms  disappears ;  let  a  carbon 
atom  combine  with  two  atoms  of  oxygen,  the  total  chemical 
energy  of  the  atoms  again  disappears :  but  if  the  carbon  atom 
possesses  four  '  units  of  affinity,'  the  oxygen  atom  two  '  units 
of  affinity.'  and  the  hydrogen  atom  one  '  unit  of  affinity,'  the 
heats  of  formation  of  the  two  compound  molecules  ought  to 
be  equal;  assuming,  of  course,  that  the  heat  produced  when  the 
molecules  CH4and  CO2  are  formed  from  atoms  of  carbon  and 
hydrogen,  and  carbon  and  oxygen,  respectively,  measures  the 
total  loss  of  chemical  energy  which  occurs  in  these  processes. 
But  the  differences  between  the  heats  of  formation  of  carbon 
compounds  shew  that  the  expression  '  the  carbon  atom  has 
four  units  of  affinity'  cannot  mean  that  the  chemical  energy 
of  the  carbon  atom  is  divisible  into  four  parts,  unless  indeed 
the  unit  of  affinity  is  variable,  and  is  varied  for  each  com- 
bination of  carbon  with  other  atoms1. 

(4)  The  carbon  atom  has  four  equivalencies.     Can  this 
mean  that  the  atom  exerts  force  in  four  directions  ?     A  so- 
called  'valency'  is  then  a  direction.     But  there  is  no  force 
exerted  till  the  mutual  atomic  transaction  begins;  the  carbon 
atom  considered  alone  has  therefore  no  '  valencies.'    Take  the 
molecule  CO;  force  is  exerted  by  the  carbon  on  the  oxygen 
atom;   the  remaining  'valencies'  are  sometimes  said  to  be 
'  mutually  satisfied,'  i.e.  on  the  present  hypothesis,  the  carbon 
atom  in  the  molecule  CO  exerts  force  in  two  directions  on 
itself;   but  here  again  we  have  the  hypothesis  of  the  non- 
homogeneity  of  the  carbon  atom,  and  the  existence  of  active 
and  inactive  parts  in  that  atom. 

(5)  In   the  vibration  of  a  carbon  atom  there  are  four 
points,  at  each  of  which  mutual  action  can  occur  between 
this  atom  and  another  atom.     On  this  supposition,  a  'double 

1  For  a  view  analogous  to  this  see  appendix  to  Section  4  of  the  present 
chapter,  par.  98. 


CHAP.  1 1.  §§6 1, 62]  ATOMIC   'BONDS.'  135 

link'  would  mean  that  mutual  action  occurs  between  the  two 
atoms  thus  linked  at  two  of  these  positions;  e.g.  the  formula 
O  =  C  =  O  would  mean  that  in  performing  a  vibration  the 
carbon  atom  acts  twice  on,  and  is  twice  acted  on  by,  each 
oxygen  atom.  But  if  so,  surely  a  'double  link'  would  imply 
molecular  stability,  whereas  it  frequently  means  the  reverse1. 
62  But  although  we  cannot  form  a  clear  physical  conception 
of  the  meaning  of  the  phrase  'the  carbon  atom  has  four 
bonds,'  and  although  such  formulae  as  C  =  O,  O  =  C  =  O, 
H2C  =  CH2,  and  HC  =  CH,  which  spring  from  the  notion  of 
atomic  bonds,  fail  to  call  up  in  the  mind  clear  images  of  the 
things  they  are  meant  to  represent,  nevertheless  it  may  be 
urged  that  inasmuch  as  the  properties  of  such  molecules  as 
CO,  CO8,  CaH4,  and  C2H2,  shew  that  the  chemical  functions 
of  the  atoms  of  carbon  vary  in  different  molecules  all  of 
which  are  composed  of  carbon  and  hydrogen  atoms  only 
or  of  carbon  and  oxygen  atoms  only,  it  is  convenient  to 
express  such  variations  of  function  in  our  nomenclature  and 
notation,  and  that  the  expressions  '  singly,  doubly,  and  trebly, 
linked  carbon  atoms,'  and  the  symbols  C  —  C,  C  =  C,  and 
C  =  C,  are  convenient  for  this  purpose. 

The  importance  of  expressing  undoubted  chemical  facts 
in  simple  terms  and  of  representing  these  facts  in  consistent 

1  A  view  different  from  any  of  the  preceding  has  been  suggested  by  Pickering 
(C.  S.  Proc.  1885.  122),  and  also  by  Armstrong  (Proc.  £.  S.  1886.  268;  Nature, 
35.  570) ;  but  the  view  appears  to  me  to  involve  the  use  of  the  term  valency  as 
synonymous  with  affinity  of  atoms,  and  therefore  to  call  for  discussion  rather  in  the 
chapter  on  affinity  than  in  the  present  place.  In  his  Ansichten  iiber  die  organische 
Chemie  (part  I.,  pp.  2 — 5),  van't  Hoff  regards  the  chemical  interactions  of  atoms  as 
a  consequence  of  gravitation.  He  shews  that  if  the  form  of  an  atom  is  not  spherical 
the  intensity  of  the  attraction  of  that  atom  for  other  atoms  must  be  marked  by  a 
definite  number  of  maximum  points  on  the  surface  of  the  atom,  which  maxima 
depend  on  the  form  of  the  atom,  and  may  have  different  values.  The  number  of 
these  maxima  is  regarded  by  van't  Hoff  as  expressing  the  valency  of  the  atom.  As 
the  atom  vibrates  its  form  will  undergo  change;  hence  the  valency  of  an  atom  may 
vary  with  variations  in  the  state  of  motion  of  the  atom,  and  these  variations  will  be 
conditioned  by  temperature,  nearness  to  other  atoms,  &c.  On  this  view,  a  combina- 
tion of  atoms,  that  is  a  molecule,  must  possess  a  certain  valency,  which  is  conditioned 
by  the  special  arrangement  of  its  parts,  but  is  not  necessarily  the  same  as  the 
valency  of  any  of  these  parts.  On  the  subject  of  'double  bonds '  see  also  appendix 
to  Section  4  of  this  chapter. 


136  ATOMIC   AND   MOLECULAR   SYSTEMS.          [BOOK  I. 

formulae  is  admitted  by  all  chemists.  Those  chemists  who 
oppose  the  use  of  formulae  and  terms  based  on  the  hypothesis 
of  atomic  bonds  assert,  and  I  think  rightly  assert,  that  the 
facts  supposed  to  be  expressed  by  single,  double,  and  treble 
.linkings  are  more  simply  and  as  forcibly  expressed  by  for- 
mulae arising  out  of  the  three  fundamental  notions  of  atomic 
valency;  which  are  (i)  that  each  atom  in  a  molecule  directly 
interacts  with  a  limited  number  of  other  atoms  ;  (2)  that  the 
maximum  number  of  atoms  with  which  any  specified  atom 
directly  interacts  is  measured  by  the  maximum  number  of 
atoms  of  hydrogen,  fluorine,  chlorine,  bromine,  or  iodine, 
with  which  the  atom  in  question  combines  to  form  a  gaseous 
molecule;  and  (3)  that  an  atom  may,  and  frequently  does, 
directly  interact  with  a  smaller  number  of  other  atoms  than 
is  expressed  by  its  maximum  valency.  Instead  of  saying, 
'the  two  carbon  atoms  in  the  molecule  of  ethane  (C2H6)  are 
singly  linked,  the  two  carbon  atoms  in  the  molecule  of 
ethylene  (C2H4)  are  doubly  linked,  and  in  the  molecule  of 
acetylene  (C2H2)  the  two  carbon  atoms  are  trebly  linked,' 
these  chemists  say,  '  the  molecule  of  ethane  contains  a 
pair  of  tetravalent  carbon  atoms,  the  molecule  of  ethylene 
contains  a  pair  of  trivalent  carbon  atoms,  and  the  molecule 
of  acetylene  contains  a  pair  of  divalent  carbon  atoms';  and 
instead  of  the  symbols  H2C  =  CH2  and  HC  =  CH,  they  use 
the  symbols  H2C  -  CH2  and  HC  -  CH.  All  that  is  expressed 
or  suggested  by  the  first  pair  of  formulae  is  expressed  and 
suggested  by  the  second,  and  the  latter  have  the  great 
advantage  of  being  based  on  a  definite  and  self-consistent 
hypothesis  of  atomic  valency,  whereas  the  former  rest  to  a 
great  extent  only  on  words  and  phrases. 

The  expressions  '  single,  double,  and  treble  linkings,' 
'  mutual  satisfaction  of  units  of  affinity,'  and  the  like,  imply 
the  possession  of  knowledge  which  at  present  we  do  not 
possess. 

The  notion  of  units  of  affinity,  or  valencies1,  or  bonds, 
has  been  carried  too  far.  It  appears  at  first  sight  to  give 

1  It  is  important  to  distinguish  between   the   expression   'valency'  and   'a 
valency.' 


CHAP.  II.  §§62, 63]       EQUIVALENCY  OF  ATOMS.  137 

a  dynamical  explanation  of  the  structure  of  molecules,  but 
it  has  forgotten  the  two-sidedness  of  atomic  transactions;  it 
apparently  affords  a  means  of  measuring  atomic  forces,  but 
it  has  used  a  unit,  undefined  except  as  a  quantity  changeable 
at  pleasure;  it  appears  to  simplify  chemical  formulae,  but  it 
has  really  made  them  harder  to  understand  by  grafting  on  to 
the  definite  conception  of  atom  the  vague  and  unnecessary 
notion  of  'bond.' 

63  The  valencies  of  the  atoms  of  about  three-fifths  of  the 
elements  can  be  regarded  as  fairly  well  established.  The 
data  required  for  determining  the  valency  of  an  elementary 
atom  are,  the  analysis,  and  determination  of  the  molecular 
weight,  of  more  than  one  gasifiable  compound,  the  molecule 
of  each  of  which  compounds  is  composed  of  a  single  atom  of 
the  specified  element  combined  with  monovalent  atoms  only, 
that  is  combined  with  atoms  of  hydrogen,  chlorine,  bromine, 
iodine,  or  fluorine,  only. 

Many  non-gasifiable  compounds  containing  monovalent 
atoms  combined  with  atoms  of  a  single  other  element  are 
known  (e.g.  many  metallic  haloid  compounds):  if  the  reacting 
weights  of  these  solid  compounds,  as  deduced  by  the  aid  of 
considerations  such  as  those  sketched  on  pp.  78 — 85,  are 
assumed  to  be  the  true  relative  weights  of  the  molecules  of 
these  compounds ;  and  if  those  generalisations  which  have 
been  made  concerning  the  arrangement  of  atoms  in  gaseous 
molecules  are  assumed  to  hold  good  for  the  reacting  weights 
of  solids  also ;  then  the  valency  of  many  elementary  atoms 
not  included  in  the  table  on  p.  127  can  be  determined. 
Thus,  if  we  assume  that  the  general  formula  MX  represents 
the  atomic  structure  of  the  molecules  of  the  solid  haloid 
salts  of  the  alkali  metals,  (M  =  K,  Na,  Li,  &c.  and  X  =  F, 
Cl,  Br,  or  I)  then  the  atoms  of  these  metals  are  most 
probably  monovalent.  Most  of  the  generally  accepted  for- 
mulae for  salts  of  alkali  metals  may  be  written  with  the 
atoms  of  these  metals  represented  as  each  in  direct  com- 
bination with  only  one  other  atom ;  but  whenever  this 
arrangement  has  become  somewhat  unsatifactory  chemists 
have  not  hesitated  to  assume  that  the  atoms  of  the  alkali 


138  ATOMIC   AND   MOLECULAR   SYSTEMS.  [BOOK  I. 

metals  may  be  tri-  penta-  or  even  heptavalent,  i.e.  may  each 
act  on,  and  be  acted  on  by,  3,  5,  or  7  other  atoms.  So  with 
other  elements ;  from  a  consideration  of  solid  or  liquid  com- 
pounds only  no  trustworthy  conclusions  as  to  the  valencies  of 
the  atoms  in  the  molecules  of  these  compounds  can  be  deduced. 
It  is  so  easy,  after  making  the  two  fundamental  assumptions 
stated  above,  to  make  an  indefinite  number  of  further  assump- 
tions; it  becomes  so  pleasant  to  manipulate  formulae  on 
paper,  that  it  is  certainly  better,  in  the  present  state  of 
knowledge,  to  determine  the  valencies  of  atoms  altogether 
from  the  study  of  gaseous  molecules.  It  is  very  probable 
that  the  valency  of  the  elementary  atoms  varies  periodically 
with  variations  in  the  relative  weights  of  these  atoms :  if  this 
general  statement  is  thoroughly  established,  the  exact  nature 
of  the  periodic  function  is  determined,  and  the  true  atomic 
weights  of  all  the  elements  are  fixed,  we  shall  have  in  the 
Periodic  Law  a  most  important  method  for  determining 
atomic  valencies.  But  a  great  deal  of  work  must  be  done 
before  this  '  law '  can  be  applied  otherwise  than  generally  and 
tentatively  to  questions  of  valency  (see  chap.  III.  par.  1 14). 

SECTION  IV.     Allotropy  and  Isomerism. 

64  Having  gained  the  conception  of  a  molecule  as  composed 
of  atoms  each  directly  interacting  with  a  definite  number  of 
other  atoms,  we  at  once  regard  the  molecule  as  a  structure ; 
we  recognise  what  Frankland  in  1852  happily  called  'limited 
molecular  mobility.'  A  structure  involves  arrangement  of 
parts  and  subordination  of  less  to  more  important  parts ;  it 
supposes  the  existence  of  definite  actions  for  fulfilling  which 
the  structure  is  adapted  ;  in  a  word,  structure  means  cor- 
relation of  properties  with  material  configuration1. 

1  When  'arrangement  of  atoms  in  the  molecule'  is  spoken  of,  or  when  a 
similar  phrase  is  used,  it  is  to  be  taken  as  implying  only  a  rough  approximation 
to  a  knowledge  of  atomic  arrangements.  Structural  formulas  sum  up  facts  of 
formation  and  decomposition,  and,  assuming  the  fundamental  positions  of  the 
molecular  and  atomic  theory,  and  also  the  hypothesis  of  valency,  these  formulae 
exhibit,  in  a  rough  and  general  way,  connexions  between  these  facts  and  the 
directions  of  the  mutual  interactions  of  the  atoms  in  the  molecules  of  the  compounds 


CHAP.  II.  §§64 — 66]      MOLECULAR  STRUCTURE.  139 

And  when  we  consider  the  properties  of  individual  mole- 
cules the  justness  of  thus  regarding  each  as  a  definite  atomic 
structure  becomes  more  apparent.  We  find  many  compound 
molecules  composed  of  the  same  number  of  the  same  atoms 
and  yet  exhibiting  markedly  different  chemical  and  physical 
properties,  i.e.  we  find  the  phenomenon  of  Isomerism:  how  can 
we  account  for  this  except  by  assuming  (i)  that  each  mole- 
cule has  a  definite  atomic  structure,  and  (2)  that  the  same 
atoms  may  be  differently  arranged  in  different  molecules? 

65  A  knowledge  of  the  atomic  configurations  of  series  of 
molecules,  supposing  this  to  be  gained,  must  be  supplemented 
by  a  knowledge  of  the  way  in   which  the  energy  of  each 
molecule   varies   with   variations    in    the   configuration    and 
motion  of  its  constituent  atoms,  before  a  complete  knowledge 
of  the  dynamical  properties  of  these  molecules  is  possible. 
But  chemistry  is  yet  far  from  this  goal ;  she  is  obliged  to  be 
content  with  a  very  partial  and  sometimes  very  vague  know- 
ledge concerning  the  atomic  configurations  of  a  few  mole- 
cules ;  she  has  hardly  entered  on  the  second  part  of  her  task. 

66  Granting  then  that  variations  in  the  properties  (chemical 
and  physical)  of  molecules  accompany  variations  in  the  con- 
figurations of  the  atoms  which  build  up  these  molecules,  it  is 
conceivable  that  the  latter  variations  may  consist  in 

(i)  variations  in  the  relative  positions  of  the  atoms, 
or     (2)  variations  in  the  distances  between  the  atoms,  their 
relative  positions  being  constant. 

To  illustrate  this  point  let  us  take  the  molecule  CaH6O. 
More  than  one  compound  exists  the  molecules  of  which 
have  the  atomic  composition  expressed  by  this  formula.  On 
the  first  assumption,  viz.  that  variation  of  properties  is  to  be 
correlated  with  variations  in  the  relative  positions  of  the 
atoms  in  the  molecule,  the  atoms  being  represented  as  arranged 
all  in  the  same  plane,  we  find  that  there  are  two  possible 
arrangements  of  two  carbon,  six  hydrogen,  and  one  oxygen, 

formulated,  the  atoms  being  represented  in  the  formulae  as  situated  all  in  the  same 
plane.  No  attempt  is  made  in  these  formulae  to  express  quantitative  measure- 
ments of  atomic  interactions. 


140  ATOMIC   AND   MOLECULAR   SYSTEMS.          [BOOK  I. 

atoms  (assuming  the  valency  of  the  carbon,  hydrogen,  and 
oxygen  atom  to  be  4,  i,  and  2  respectively),  viz. ; 

(a)  H      H  (b]  H  H       . 

II  II 

H  — C  — C  — O  — H,  H  — C  — O-C  — H. 

II  I  I 

H     H  H  H 

Hence,  on  the  first  assumption,  two  compounds  each 
having  the  composition  expressed  by  the  empirical  formula 
C2H6O  may  exist. 

But  if  we  make  the  second  assumption,  viz.  that  variation 
of  properties  is  to  be  correlated  with  variations  in  the  dis- 
tances between  the  atoms  in  the  molecule,  the  relative  posi- 
tions of  these  atoms  remaining  unchanged,  we  may  have 
an  apparently  unlimited  number  of  compounds  of  the  for- 
mula C2H6O ;  such  compounds  might  perhaps  be  repre- 
sented in  this  way  : — 

(a)        H     H  (£)          H     H 

II  II 

H  — C  — C  — O  — H,  H C  — C O  — H, 

II  II 
H     H 

H     H 

(c)            H  H 


H  — C C— O  — H, 


I 
H  H 

and  so  on. 

Now  as  only  two  compounds  having  the  composition 
C2H6O  are  known  to  exist,  we  have  a  presumption  in  favour 
of  the  first  supposition :  much  stress  cannot  however  be  laid 
on  this  argument.  Moreover  if  the  second  of  the  two  suppo- 
sitions is  correct,  then  any  molecule  composed  of  two  atoms 
should  be  capable  of  existing  in  more  than  one  modification ; 
in  other  words,  every  diatomic  molecule  should  be  capable 
of  shewing  isomerism.  But  there  is  no  certainly-established 
instance  of  isomerism  exhibited  by  a  molecule  composed 
of  less  than  three  atoms  ;  therefore,  as  the  assumption  that 
variations  of  properties  exhibited  by  compounds  having  the 


CHAP.  II.  §§  66,  67]         ALLOTROPY   AND   POLYMERISM.  141 

same  composition  and  the  same  molecular  weight  are  con- 
nected with  variations  in  the  relative  positions  of  the  atoms 
composing  the  molecules  of  these  compounds  suffices  to 
explain  the  vast  majority  of  well-authenticated  cases  of  iso- 
merism  among  gaseous  molecules,  we  conclude  that  it  is 
better,  at  any  rate  at  present,  to  build  the  general  theory 
of  isomerism  on  this  hypothesis1. 

67  But  before  more  fully  considering  this  subject,  it  will  be 
well  to  glance  at  the  allied  phenomena  of  allotropy  and 
polymerism. 

The  table  on  p.  45  shews  that  of  the  sixteen  elements 
whose  molecular  weights  have  been  determined  by  the  help 
of  Avogadro's  law,  six,  viz.  oxygen,  sulphur,  selenion,  iodine, 
phosphorus,  and  arsenic  (probably  bromine  also),  possess  a 
smaller  molecular  weight  at  high  than  at  lower  tempera- 
tures : — the  number  of  atoms  in  the  molecule  of  oxygen 
at  temperatures  below  about  300°  and  under  special  con- 
ditions is  3,  at  temperatures  above  300°  it  is  2  ;  the  molecule 
of  sulphur  at  temperatures  not  much  higher  than  the  boiling 
point  of  that  element  is  composed  of  6  atoms,  and  at  some- 
what higher  temperatures  of  2  atoms;  the  number  of  atoms  in 
the  molecule  of  selenion  varies  from  3  to  2,  in  the  molecule 
of  iodine  (and  probably  also  in  that  of  bromine)  from  2  to  I, 
and  in  the  molecules  of  phosphorus  and  arsenic  from  4  to  2, 
according  to  temperature.  We  know  that  the  properties  of 
the  triatomic  molecule  O3  differ  much  from  those  which  cha- 
racterise the  diatomic  molecule  O2 ;  no  experiments  have 
been  made  to  compare  the  properties  of  the  hexatomic  with 
those  of  the  diatomic  molecules  of  sulphur,  of  the  triatomic 
with  the  diatomic  molecules  of  selenion,  of  the  diatomic  with 
the  monatomic  molecules  of  iodine,  or  of  the  tetratomic 
with  the  diatomic  molecules  of  phosphorus  or  arsenic. 

Of  the  15  or  16  nonmetallic  elements,  phosphorus   and 

1  The  supposition  that  isomerism  may  be  due  to  variations  in  the  distances 
between  atoms  the  relative  positions  of  which  remain  unchanged,  appears  to  be 
opposed  to  the  results  of  physical  experiments  which  are  in  agreement  with 
deductions  made  from  the  kinetic  theory  of  gases.  See  Lessen,  Annalen,  204, 
p.  269. 


142  ATOMIC  AND   MOLECULAR   SYSTEMS.          [BOOK  I. 

arsenic,  boron,  carbon  and  silicon — besides  sulphur  and  sele- 
nion — exhibit  marked  variations  in  physical  and  chemical 
properties  when  in  the  solid  state.  We  are  not  justified 
in  unconditionally  asserting  that  these  variations  of  pro- 
perties accompany  differences  in  the  atomic  configurations 
of  the  molecules,  or  differences  in  the  numbers  of  atoms  in 
the  molecules,  of  red  and  yellow  phosphorus,  or  of  octahe- 
dral and  prismatic  sulphur,  &c.  When  the  differences  in 
properties  are  chiefly  physical  (e.g.  differences  in  crystalline 
form,  in  specific  gravity,  in  melting  points,  &c.),  they  very 
probably  may  be  correlated  with  differences  in  the  molecular, 
rather  than  in  the  atomic,  configurations  of  the  various  modi- 
fications of  the  element  in  question  \ 

Be  this  however  as  it  may,  the  differences  experimentally 
shewn  to  exist  between  the  properties  of  the  molecules  of 
gaseous  oxygen  and  ozone  are  explicable  in  terms  of  the 
molecular  theory  only  by  admitting  that  the  properties  of 
a  molecule  are  dependent  not  only  on  the  nature  but  also 
on  the  number  of  the  atoms  which  compose  it2. 
68  The  names  allotropy  and  polymerism  are  applied  to  ana- 
logous phenomena  exhibited  by  elements  and  compounds 
respectively3.  In  the  preceding  paragraph  we  have  had 

1  See  Section  5  of  present  chapter. 

-  It  ought  to  be  noted  that  change  from  one  allotropic  form  to  another  is 
accompanied  by  production  or  disappearance  of  heat;  se&post,  chap.  IV.,  par.  125. 
There  are  some  interesting  observations  bearing  on  the  subject  of  allotropy  by 
W.  Spring  in  the  Berichte  [see  especially  16.  1002 — 3].  Spring  finds  that  when  an 
element  which  exhibits  allotropy  is  subjected  to  great  pressure,  that  modification 
which  has  the  greatest  specific  gravity  is  produced.  Yellow  phosphorus  is  changed 
into  red  by  compression  :  red  phosphorus  and  sulphur  do  not  combine  until  heated 
to  260°,  i.e.  to  the  temperature  at  which  red  is  changed  to  yellow  phosphorus;  red 
phosphorus  does  not  combine  with  sulphur  when  the  two  are  subjected  to  a 
pressure  of  6500  atmospheres,  at  which  pressure  many  metallic  sulphides  are 
produced.  Hence  Spring  concludes  that  red  phosphorus  is  less  chemically  ener- 
getic than  yellow;  and  generally  that  the  more  a  solid  substance  is  rendered 
dense  the  more  is  its  chemical  activity  decreased.  Red  phosphorus  he  regards  as 
a  polymeride  of  yellow  phosphorus. 

3  The  term  allotropy  is  sometimes  applied  to  compounds  as  well  as  to  elements, 
to  express  the  existence  of  two  or  more  forms  of  the  same  solid  compound ;  thus 
arsenious  oxide  crystallises  in  two  distinct  forms,  and  the  change  from  one  of  these  to 
the  other  is  sometimes  said  to  be  an  allotropic  change.  Allotropy  as  thus  applied 
to  compounds  is  synonymous  with  physical  isomerism  (s.  post,  par.  101).  The 


CHAP.  II.  §§  68, 69]  POLYMERISM.  1 43 

examples  of  allotropy,  let  us  now  consider  a  few  examples 
of  polymerism. 

If  two  molecules  exist  consisting  of  the  same  elementary 
atoms  but  one  heavier  than  the  other,  the  heavier  molecule  is 
said,  in  certain  cases,  to  be  a  '  polymeric  modification'  or 
a  '  polymeride '  of  the  other :  thus  C^H^  is  a  polymeride  of 
C8H10,  C]5H24  is  a  polymeride  of  C10H,a,  H3C3N3O3  is  a  poly- 
meride of  HCNO,  C6H]2O3  is  a  polymeride  of  C2H4O.  Glu- 
cose, .rC6H12O6,  is  not  however  regarded  as  a  polymeride  of 
acetic  acid,  C2H4Oa:  the  name  is  restricted  to  those  mole- 
cules whose  mass  is  a  multiple  of  that  of  other  molecules, 
and  which  are  obtained  by  simple  reactions  from  these  other 
molecules.  Thus  ethaldehyde,  CaH4O,  is  easily  polymerised 
(e.g.  by  the  action  of  a  very  little  hydrochloric  or  sulphuric 
acid)  with  formation  of  parethaldehyde,  C6H12O8:  but  the 
latter  body  is  not  directly  obtainable  from  ethylene  oxide, 
although  the  molecule  of  this  compound,  like  that  of  ethalde- 
hyde, is  composed  of  2  atoms  of  carbon,  4  of  hydrogen,  and 
I  of  oxygen  ;  therefore  parethaldehyde  is  not  called  a  poly- 
meride of  ethylene  oxide. 

But  few  examples  of  undoubted  polymerism  are  fur- 
nished by  compounds  of  the  elements  other  than  carbon  : 
one  of  the  most  marked  cases  is  the  molecule  N2O4  which 
is  a  polymeride  of  NO2;  another  instance  is  furnished  by  the 
molecules  Sn2Cl4  and  SnCly 

69  Let  us  now  turn  to  the  subject  of  isomerism.  This  term 
is  applied  to  the  existence  of  molecules  characterised  by 
different  properties  but  composed  of  the  same  number  of 
the  same  atoms. 

Isomeric  compounds  are  generally  said  to  be  metameric 
when  they  belong  to  different  chemical  types.  This  state- 
ment does  not  of  course  furnish  a  definition  of  metameric 
compounds;  but  it  is  sufficient.  Various  hydrocarbons,  all 
possessed  of  the  general  properties  of  paraffins  but  each 
differing  in  some  properties,  chemical  and  physical,  from  the 
others,  are  represented  by  the  formula  C6H14 :  various  hydro- 
art.  Allotropy  in  ihe  new  edition  of  Waltz's  Dictionary  should  be  read  by  the 
student. 


144  ATOMIC   AND   MOLECULAR   SYSTEMS.          [BOOK  I. 

carbons,  all  benzenes,  but  each  characterised  by  its  own  special 
properties,  are  represented  by  the  formula  C8H10:  the  different 
paraffins  (C6H14)  or  the  different  benzenes  (C8H10)  are  said  to 
be  isomerides  one  of  the  other.  But  although  two  molecules 
are  represented  by  the  formula  C2H6O  yet  these  belong  to 
very  different  types  or  groups  of  compounds,  one  is  a  pri- 
mary alcohol,  the  other  is  an  ether ;  so  again  allylic  alcohol 
and  dimethyl  ketone  have  both  the  formula  C3HgO,  but  these 
bodies  are  altogether  distinct  in  their  chemical  properties: 
such  compounds  are  said  to  be  metameric.  Metamerides 
are  thus  seen  to  be  a  sub-class  included  in  the  larger  class  of 
isomeric  compounds. 

A  few  inorganic  compounds  exhibit  phenomena  which 
may  be  explained  by  supposing  the  existence  of  isomeric 
molecules,  but  it  is  only  when  we  study  the  compounds 
of  carbon  that  we  are  obliged  to  admit  that  molecules  may 
be  composed  of  the  same  numbers  of  the  same  atoms  but 
differ  in  chemical  and  physical  properties. 

70  The  hypothesis  of  atomic  valency  having  led  to  the  re- 
cognition of  the  molecule  as  a  structure  may  be  carried 
further ;  it  may  guide  us  in  determining  the  probable  relative 
structures  of  isomeric  molecules  (see  note  to  p.  138). 

If  it  be  granted  that  isomerism  is  correlated  with  different 
relative  positions  of  atoms,  but  not  with  different  distances 
between  atoms  in  the  same  relative  positions  in  the  molecule, 
(see  p.  139)  it  follows  that  a  molecule  composed  of  not  more 
than  two  atoms  cannot  exhibit  isomerism1. 

The  maximum  number  of  monovalent  atoms  which  can 
be  combined  with  polyvalent  atoms  in  a  molecule  is  found 
by  the  formula2 

n\  —  H3  +  2W4  +  3;/5  +  4W6  +  2> 

where  «t,  «3,  «4,  &c.  represent  the  numbers  of  monovalent, 
trivalent,  tetravalent,  &c.  atoms  in  the  molecule.  In  any  mole- 
cule in  which  the  value  of  «,  agrees  with  that  deduced  by 
this  formula  each  polyvalent  atom  must  necessarily  directly 

1  Such  formulae  as  O  =  N  -  and  =  N  -  O  -  are  really  at  present  the  same. 

2  See  Lothar  Meyer,  Die  Modernen  Theorien  der  Chemie  (4th  Ed.),  p.  218 
et  sef.,  or  English  Edition  [Modern  Theories  of  Chemistry},  p.  198  et  seq.,  of  which 
pages  free  use  has  been  made  in  these  paragraphs. 


CHAP.  II.  §§  70,  71]  ISOMERISM.  145. 

interact  with  the  maximum  number  of  monovalent  atoms. 
Such  molecules  are  said  to  be  saturated;  they  cannot  directly 
combine  with  monovalent  atoms.  Examples  of  saturated 
molecules  are  furnished  by  C2H6,  C8H8,  C2H5C1,  C3H6C12,  &c. 
But  in  the  molecules  C2H4,  C2H2,  C6H6,  and  in  many  other 
molecules,  the  number  of  monovalent  atoms  is  less  than  that 
expressed  by  the  formula  just  given.  In  these  molecules 
each  polyvalent  atom  directly  interacts  with  less  than  the 
maximum  number  of  monovalent  atoms.  Such  molecules 
are  said  to  be  unsaturated.  Unsaturated  molecules  are 
generally  able  to  combine  directly  with  monovalent  atoms. 

The  language  in  which  the  facts  of  isomerism  are  generally 
expressed  speaks  of  some  of  the  polyvalent  atoms  in  unsatu- 
rated  molecules  as  being  '  linked  by  double  or  treble  bonds ' ; 
the  language  which  springs  from  the  view  of  valency  adopted 
in  this  book  (the  view  is  essentially  that  of  Lessen)  speaks 
of  some  of  the  polyvalent  atoms  in  unsaturated  molecules 
as  exhibiting  in  these  molecules  less  than  their  maximum 
valency. 

Thus  to  take  the  unsaturated  molecules  C2H4  and  C2H2 : 
the  expression  in  common  use  is  'the  carbon  atoms  in  the 
molecule  C2H4  are  joined  by  a  double  bond,  and  in  the  mole- 
cule C2H2  by  a  treble  bond';  and  this  expression  is  embodied 
in  the  formulae  H2C  =  CH2  and  HC  =  CH:  the  expression 
used  by  the  upholders  of  Lossen's  conception  of  atomic 
valency  is  '  the  carbon  atoms  in  the  molecule  C2H4  are  tri- 
valent,  and  in  the  molecule  C2H2  the  carbon  atoms  are  di- 
valent ' ;  and  this  expression  is  embodied  in  the  formulae 
H2C  —  CH2  and  HC  —  CH.  The  expressions  'a  pair  of  doubly 
linked  carbon  atoms '  and  '  a  pair  of  trebly  linked  carbon 
atoms '  are  respectively  synonymous  with  the  expressions  '  a 
pair  of  trivalent  carbon  atoms '  and  '  a  pair  of  divalent  carbon 
atoms ' :  each  term  used  in  the  latter  expressions  has  an 
accurate  meaning  defined  once  for  all ;  the  meanings  given 
to  the  terms  '  doubly  linked '  and  '  trebly  linked '  atoms 
depend  upon  the  views  of  the  chemist  who  employs  them. 
71  The  number  of  ways  in  which  the  atoms  comprising  a 
complex  molecule  may  be  arranged,  in  accordance  with  the 
M.  c.  10 


146  ATOMIC    AND   MOLECULAR   SYSTEMS.          [BOOK  I. 

limitations  imposed  by  the  hypothesis  of  atomic  valency,  is 
evidently  very  great  ;  to  determine  the  maximum  number  of 
possible  isomerides  of  a  given  formula  is  a  purely  mathe- 
matical problem1.  At  present  we  seem  justified  in  con- 
cluding that  many  atomic  configurations  which  are  mathe- 
matically possible  are  physically  impossible;  this  is  equivalent 
to  saying  that  the  stability  of  molecules  does  not  depend 
solely  on  the  valencies  of  their  constituent  atoms.  To  deter- 
mine which  of  the  possible  configurations  of  a  given  number 
of  atoms  are  stable  ;  to  generalise  the  connexions  undoubtedly 
existing  between  molecular  structure  and  stability,  and  also 
between  this  structure  and  the  functions  of  the  molecule  or 
of  parts  thereof;  this  is  the  task  that  chemists  are  now 
elaborating. 

72  The  molecular  formula  of  a  compound  sometimes  of  itself 
gives  us  a  considerable  amount  of  information  regarding  the 
structure  of  the  molecule  of  that  compound.     Thus  we  appear 
justified,   at    present,    in    making    the   following    assertions  : 
(i)   molecules  composed  of  monovalent  atoms  only  cannot 
exhibit  isomerism  ;  (2}  molecules  composed  of  a  single  poly- 
valent atom  united  with  monovalent  atoms  only  cannot  ex- 
hibit isomerism  ;  (3)  isomerism  cannot  be  exhibited  by  mole- 
cules composed  of  two  polyvalent  atoms  united  with  mono- 
valent atoms,  provided  the  latter  are  all  atoms  of  the  same 
element,  or  all  but  one  atoms  of  the  same  element,  when  the 
two   polyvalent   atoms   are   themselves   atoms  of  the   same 
element. 

73  Any  molecule  composed  of  more  than  two  atoms  and  not 
belonging  to  one  of  the  classes  above  defined  may  exhibit 
isomerism.    The  possible  variations  of  structure  even  in  mole- 
cules composed  of  a  small  number  of  atoms  may  be  large. 
Thus  N2O  may  have  any  of  the  structures 

(i)  N  —  N,  or    (2)  N  —  N  —  O,  or    (3)  N  —  O  —  N  ; 


1  Prof.  Cayley,  Brit.  Ass.  Reports  for  1875.  257,  examined  the  relations  between 
the  number  of  carbon  atoms  in  the  molecules  of  paraffins  and  the  number  of 
isomeric  modifications  of  each  molecule  allowed  by  the  hypothesis  of  valency  ;  thus 

number  of  carbon  atoms  in  molecule  of  paraffin,   i.  4.  7.  10.     12.     13. 

number  of  possible  isomerides          ......         i.  2.  9.  75.  357.  799. 


CHAP.  IT.  §§  72,  73]      STRUCTURAL   FORMULAE.  147 

neither  the  nitrogen  nor  the  oxygen  atom  can  directly  inter- 
act with  more  than  two  atoms,  i.e.  neither  can  be  more  than 
divalent1.     NO  can  be  regarded  only  as  N  —  O.     NO2  may  be 
(i)  O  — N  — O,    or     (2)  O  — N  — O,    or    (3)  N  — O  — O. 

N2O4  may  have  many  structures  ;  e.g. 

(i)  O  —  N  —  N  —  O,        or        (2)  O  — N  — N— O, 

I  I  ^Q'     xox 
o     o 

or  (3)O  — N  — O  — O  — N  — O,  or  (4)  O  —  N  —  O  —  O  —  N  —  O, 
or  (5)  N  — O  — O  — O  — O— N,  or  (6)  N  — N  — O— O  — O  — O,  &c. 

The  compounds  of  carbon  present  the  best  field  for  the 
study  of  isomerism2. 

It  has  been  already  stated  that  a  molecule  composed  of 
two  carbon  (tetravalent)  atoms  united  with  five  monovalent 
atoms  of  one  element  and  one  monovalent  atom  of  another 
element,  (i.e.  a  molecule  of  the  form  C^X6X)  cannot  exhibit 
isomerism.  If  however  there  are  four  monad  atoms  of  one 
kind,  and  two  of  another  kind,  in  the  molecule  (if  the  form  of 
the  molecule  is  represented  by  the  symbol  C2X4JQ  isomerism 
becomes  possible  ;  thus  C2H4C12  may  have  the  structure 

H     H  H     H 

II  II 

Cl  — C  — C  — Cl,        or        H  — C-C  — Cl 

II  II 

H     H  H     Cl 

(or  more  shortly,  C1H2C  -  CH2C1  and  H8C  -  CHC12).  But 
when  three  carbon  atoms  combine  with  monovalent  atoms, 
the  existence  in  the  molecule  thus  produced  of  a  single 
monad  atom  different  in  kind  from  the  other  monad  atoms 
renders  isomerism  possible ;  thus  CSH7C1  (which  belongs  to 
the  general  form  CSX7X)  may  have  the  structure 

H2  H    Cl 

II  \/ 

H3C  —  C  —  CH2C1        or        H3C  —  C  —  CH3. 

1  Lossen's  nomenclature  and  notation  are  used  here  and  generally  throughout 
the  rest  of  this  book. 

2  The  subject  of  the  constitution  of  compounds  is  considered  very  fully  and 
clearly  in  the  3rd  edition  of  Remsen's  Theoretical  Chemistry. 

10 — 2 


148  ATOMIC   AND   MOLECULAR   SYSTEMS.         [BOOK  I. 

So  also  four  molecules  C3H6C12,  five  molecules  C3H6C18,  six 
C8H4C141,  five  C3H3C1S,  &c.  may  exist.  Molecules  composed 
of  four,  or  more  than  four,  atoms  of  carbon  combined  with 
monovalent  atoms  may  exhibit  isomerism  even  when  all  the 
monad  atoms  are  of  one  kind,  (i.e.  molecules  of  the  general 
form  C4X10) ;  thus  C4H10  may  have  the  structure 

H2    H2  H  CH3 

II       II  I  / 

H3C-C  — C-CH3        or        H3C  — C 

XCH3 

Molecules  composed  of  five  carbon  atoms  combined  with 
other  atoms  may  have  the  carbon  atoms  arranged  in  three 
ways,  as  represented  by  the  formulae 

C 

C— C  — C  — C  — C,         C  — C  — C  — C,        and     C  — C  — C. 

I  I 

C  C 

When  six  carbon  atoms  are  present  in  the  molecule  these 
atoms  may  be  arranged  in  five  ways,  viz. 

C  — C  — C  — C  — C  — C,     C  — C  — C  — C  — C,     C  — C  — C  — C  — C, 

I  I 

C  C 

C 

I 

C  — C  — C  — C,         C  — C  — C  — C. 

I     I  I 

C      C  C 

When  eight  carbon  atoms  are  present,  they  may  be  arranged 
in  1 8  different  ways,  &c.  The  maximum  number  of  mono- 
valent atoms  which  can  be  combined  with  any  of  these 
arrangements  of  carbon  atoms  is  found  by  the  formula 
«j  =  2«4  +  2  where  n4  =  number  of  carbon  atoms2.  But  all 
the  carbon  atoms  in  a  molecule  are  not  necessarily  tetrava- 
lent  in  that  molecule  (in  the  ordinary  nomenclature  some  of 


1  Viz.        CH2C1        CHC12        CC13        CHC12  CC13  CH3 

CC12  CH2  CHC1      CHC1  CH2  CC12 

CHaCl        CHC12        CH3         CH2C1  CH2C1  CHC1,. 

2  See  Lothar  Meyer,  loc.  cit.  pp.  240 — 242. 


CHAP.  II.  §  73]          STRUCTURAL   FORMULA.  149 

the  carbon  atoms  may  be  doubly  or  trebly  linked  to  one 
another,  or  there  may  exist  '  free  affinities  ').  Now  the  gene- 
ral formula  given  on  p.  144,  viz. 


shews  that  the  maximum  number  of  monad  atoms  in  such 
a  molecule  is  dependent  only  on  the  number  of  trivalent 
and  tetravalent,  and  is  independent  of  the  number  of  diva- 
lent, carbon  atoms  in  the  molecule.  But  in  applying  this 
formula  it  is  assumed  that  the  number  of  carbon  atoms 
which  are  actually  trivalent,  and  of  those  which  are  actually 
tetravalent,  in  any  given  molecule,  can  be  determined.  It 
is  better  to  represent  the  molecule  of  a  carbon  compound,  if 
possible,  as  containing  only  tetravalent  carbon  atoms:  in 
many  cases  however  this  cannot  be  done  ;  in  any  case  the 
reactions  of  the  compound  must  be  studied  before  a  formula 
is  given  to  it. 

Let  us  suppose  we  are  required  to  assign  formulae  to 
compound  molecules  containing  carbon,  hydrogen,  and  oxygen 
atoms.  When  the  equation  «t  =  2#4  +  2  is  satisfied,  the  struc- 
tural formula  assigned  to  the  molecule  must  evidently  con- 
tain only  tetravalent  carbon  atoms  ;  several  such  formulae 
may  however  be  possible  ;  thus  for  the  molecule  C3H8O  two 
structural  formulas  fulfil  the  conditions  required  :  — 

Hg      ri2      Hg  Ho      Ho  Ho 

III    II    II  III    II         III 

C  —  C  —  C  —  O  —  H         and        C  —  C  —  O  —  C. 

In  accordance  with  generalisations  which  have  been  made 
correlating  structure  and  properties  the  first  of  these  for- 
mulae belongs  to  a  primary  alcohol,  the  second  belongs  to 
a  mixed  ether  :  two  and  only  two  compounds  having  the 
composition  C3H8O  are  known  ;  one  exhibits  the  properties  of 
a  primary  alcohol,  the  other  those  of  a  mixed  ether. 

When  however  n^  <  2U4  +  2,  and  divalent  atoms  are  also 
present  in  the  molecule,  the  formula  may  contain  only 
tetravalent  carbon  atoms,  or  it  may  contain  tetravalent,  and 
also  di-  or  trivalent,  carbon  atoms.  Thus  in  C3HaO  «t  =  2«4  ; 


ISO  ATOMIC   AND   MOLECULAR   SYSTEMS.         [BOOK  I. 

two  structural  formulae  are  possible  for  this  molecule  wherein 
each  carbon  atom  is  tetravalent,  viz. 

(i)     H2C  — CH2  — CH2        and        (2)     H3C  —  CH  —  CH2. 

V 

Each  of  these  is  the  formula  of  an  ether ;  in  propylene 
oxide  we  have  an  ether  the  properties  of  which  shew 
that  it  is  probably  described  by  the  first  of  these  formulae. 
Six  structural  formulae  are  possible  for  the  molecule 
C3H8O,  provided  some  of  the  carbon  atoms  may  be  tri-  or 
divalent.  Three  compounds  having  this  formula  (besides 
propylene  oxide)  are  known ;  of  these,  one  is  a  ketone,  i.e. 
belongs  to  a  class  of  compounds  the  molecules  of  which  are 
generally  regarded  as  containing  a  carbon  and  an  oxygen 
atom  in  direct  union  ;  another  is  an  aldehyde,  i.e.  belongs  to 
a  class  of  compounds  the  molecules  of  which  are  regarded  as 
containing  a  carbon  atom  in  direct  combination  with  one 
oxygen  and  one  hydrogen  atom ;  and  the  third  is  an  alcohol, 
probably  a  primary  alcohol.  The  six  possible  formulae  are 


(I) 

(2) 

(3) 

(4) 

(5) 

(6) 

CH3 

CH, 

CH2 

CH3 

CH3 

CH3 

1 

1 

1 

1 

1 

c—  o 

CHS 

CH 

CH2 

C 

CH 

1 

1 

| 

1 

| 

1 

CH3         H- 

-C  —  O 

CH2 

C  —  O  —  H 

CH2 

CH 

1 

1 

1 

O  —  H 

O  —  H 

O  —  H 

The  first  and  second  formulae  contain  each  one  trivalent  carbon 
atom  and  the  oxygen  atom  is  monovalent  in  both,  the  fourth 
and  fifth  contain  each  one  divalent  carbon  atom,  and  the 
third  and  sixth  each  two  trivalent  carbon  atoms.  Formulae 
(i)  and  (2)  are  appropriated  by  dimethyl  ketone  and  pro- 
paldehyde  respectively ;  of  the  remaining  four,  (3)  and  (5) 
represent  allylic  alcohol  as  a  primary,  (6)  as  a  secondary,  and 
(4)  as  a  tertiary,  alcohol.  Judging  from  the  general  reactions 
of  allylic  alcohol  this  compound  is  probably  a  primary 
alcohol.  Formula  (3)  is  preferable  to  (5),  because  the  latter 
would  lead  us  to  expect  acetic  acid  (H3C  -  CO2H)  as  one 
of  the  products  of  oxidation  of  allylic  alcohol ;  inasmuch  as 


CHAP.  II.  §§73,  74]      STRUCTURAL   FORMULAE.  151 

acetic  acid  is  not  produced  in  this  oxidation,  formula  (3)  more 
probably  expresses  the  structure  of  the  molecule  of  allylic 
alcohol  than  any  other  possible  formula. 

74  In  these  examples  of  the  method  adopted  for  determining 
the  structural  formula  of  a  compound  several  generalisations 
concerning  the  connexion  of  structure  with  properties  have 
been  assumed.  For  instance,  it  has  been  assumed  that  if  a 
given  compound  exhibits  aldehydic  properties  the  structural 
formula  of  the  molecule  is  to  be  written  as  containing  the 
atomic  group  CHO ;  but  it  has  also  been  assumed  that  two 
structures  are  possible  for  this  group,  one  in  which  the  carbon 
atom  interacts  directly  with  the  oxygen  and  the  hydrogen 
atoms  (H  — C  — O),  and  the  other  in  which  the  carbon  atom 
directly  interacts  with  the  oxygen  atom  only  (C  —  O  —  H) ; 
further,  the  first  of  these  structures  is  assumed  to  be  corre- 
lated with  the  group  of  properties  connoted  by  the  word 
'aldehydic,'  and  the  second  with  the  properties  connoted 
by  the  expression  '  tertiary  alcoholic.'  When  therefore  a 
new  carbon  compound  is  discovered,  it  is  necessary  to  de- 
termine, as  far  as  possible,  to  what  group  of  compounds  it 
belongs ;  the  existence  of  a  certain  atomic  group  (or  groups) 
in  the  molecule  of  the  compound  may  then  generally  be 
predicated,  and  the  number  of  possible  structural  formulae 
may  thus  be  considerably  diminished.  But  the  classification 
of  the  carbon  compounds  is  certainly  not  yet  complete ; 
hence  arise  two  difficulties ;  (i)  a  new  compound  may  belong 
to  a  class  no  other  member  of  which  has  been  previously 
examined,  in  which  case  no  class-group  can  be  assigned  to 
the  formula  of  the  new  compound ;  or  (2)  a  compound  may 
be  prepared  whose  properties  indicate  that  it  belongs  to  one 
of  the  known  classes,  and  yet  the  atomic  group  which 
generally  marks  this  class  may  not  be  present  in  the  molecule 
of  this  particular  compound.  The  following  cases  may  be 
taken  as  illustrations  of  these  difficulties. 

(i)  It  was  known  that  the  interaction  of  nitrous  acid 
with  carbon  compounds  the  molecules  of  which  contained  the 
group  NH2  (amido-derivatives)  resulted  in  the  production  of 
compounds  differing  from  the  original  by  containing  OH 


152  ATOMIC  AND   MOLECULAR   SYSTEMS.          [BOOK  I. 

in  place  of  NH2;  but  when  nitrous  acid  acted  on  certain 
amido-derivatives  of  benzene,  compound  molecules  containing 
one  nitrogen  atom  more  and  two  hydrogen  atoms  less 
than  the  original  molecule  were  obtained.  The  reaction  ap- 
peared to  be  abnormal.  Several  of  the  new  compounds  were 
prepared,  their  properties  were  studied,  and  the  existence  of  a 
new  class  of  carbon  compounds  was  recognised,  the  relations 
of  which  to  other  classes  could  be  summarised  in  formulae 
containing  the  characteristic  group  —  N2— . 

(2)  As  the  result  of  long  and  varied  experience 
the  generalisation  has  been  made  that  the  molecules  of 
very  many  carbon  acids  contain  the  characteristic  group 
H  —  O  —  C  —  O  ;  but  from  time  to  time  compounds  have 
been  prepared  exhibiting  acidic  properties,  but  possessed  of 
a  molecular  structure  from  which  the  characteristic  group 
is  absent.  Thus  C3H8  yields  C3H7NO2,  and  from  this 
compound  two  isomerides  C8H6BrNO2  are  obtained,  one  of 
which  is  a  monobasic  acid,  while  the  other  does  not  shew 
acidic  properties  ;  the  possible  formulae  for  these  isomerides  are 
NO2  H2  H 

i  I        I 

(i)     H3C  — C  — CH3,        and        (2}     H3C  — C  — C  — NO2. 

Br  Br 

From  a  consideration  of  the  general  properties  of  the  two 
isomerides  and  their  relations  to  other  compounds  the  second 
formula  is  assigned  to  the  acid.  Hence  we  are  obliged  to 
conclude  that  although  most  known  carbon  acids  are  charac- 
terised by  the  atomic  group  H  -  O  -  C  -  O,  yet  a  carbon 
compound  in  the  molecule  of  which  this  group  is  not  present 
may  nevertheless  be  a  true  acid. 

A  very  instructive  example  of  the  difficulties  to  be  over- 
come before  a  general  structural  formula  can  be  assigned  to  a 
group  of  carbon  compounds,  is  afforded  by  the  investigations 
which  have  been  and  are  being  made  into  the  constitution 
of  the  quinones;  and  also  into  the  constitution  of  the 
compounds  allied  to  indigo1. 

1  See  Armstrong  and  Groves,   Organic  Chemistry,  pp.  812,  813.     Also  art. 
"Indigogruppe"  in  Ladenburg's  Handivorterbuch  der  Chemie,  Bd.  5,  p.  248. 


CHAP.  II.  §  74]         STRUCTURAL   FORMULAE.  153 

These  examples  (and  others  might  easily  be  added)  shew 
how  undesirable  it  is  to  regard  the  present  system  of  classifi- 
cation of  carbon  compounds  as  final.  As  facts  are  accumu- 
lated the  atomic  grouping  which  was  regarded  as  a  class- 
group  sometimes  becomes  the  group  of  a  larger  class, 
sub-classes  being  formed  each  characterised  by  its  special 
group  and  yet  each  containing  the  class-group.  Thus,  from 
the  analogy  between  metallic  hydroxides  and  alcohols,  and 
for  other  reasons,  the  group  O  —  H  was  assigned  to  alcohols 
(e.g.  C2H5.OH,  C3H7.OH,  &c.,  &c.);  but  it  became  evident 
that  a  sub-division  of  this  great  class  was  required  ;  facts 
were  amassed  and  formulae  devised  to  generalise  these  facts, 
until  most  chemists  are  now  agreed  that  the  molecules  of 
those  alcohols  called  '  primary '  (which  yield  certain  defi- 
nite products  when  oxidised,  &c.)  contain  the  atomic  group 
H  —  O  —  CH2,  the  molecules  of  those  called  'secondary'  (and 
which  yield  other  but  also  definite  products  when  oxidised) 
contain  the  group  H  -  O  —  C  -  H,  and  the  molecules  of  those 
called  '  tertiary'  (which  yield  a  third  distinct  set  of  products 
when  oxidised)  contain  the  group  C  —  O  —  H. 

Each  of  these  'alcoholic  groups'  itself  contains  the  group 
O  — H;  but  the  'acid  group'  H  — O-C  — O  also  contains 
this  group ;  now  we  know  that  the  function  performed  by 
hydrogen  in  an  alcoholic  molecule  is  not  the  same  as  that 
performed  by  hydrogen  in  an  acid  molecule ;  e.g.  all,  or 
some,  of  the  hydrogen  in  the  latter,  but  none  of  that  in 
the  former,  is  replaceable  by  metal  when  the  compound  is 
acted  on  by  a  metallic  carbonate ;  hence  we  infer  that  the 
function  discharged  by  a  given  atom  in  a  molecule  depends 
not  only  on  the  nature  of  that  atom,  but  also  on  the  nature  of 
the  atoms  with  which  it  is  directly,  and  indirectly,  connected 
in  the  molecule. 

In  all  the  alcoholic  groups  (viz.  H2C  -  OH,  HC  -  OH, 
and  C  —  OH)  an  atom  of  hydrogen  is  directly  connected 
with  an  oxygen  atom  which  is  again  directly  connected  with 
an  atom  of  carbon,  which  directly  interacts  with  either 
hydrogen  atoms  and  atoms  belonging  to  the  other  part  of 
the  molecule — always  either  carbon  or  hydrogen  atoms — or 


154  ATOMIC   AND   MOLECULAR   SYSTEMS.         [BOOK  I. 

only  the  latter.  In  the  acid  group  (O  —  C  —  OH)  the  carbon 
atom  with  which  the  hydrogen  atom  is  indirectly  connected 
(through  an  atom  of  oxygen)  is  itself  directly  connected 
with  an  oxygen  atom,  as  well  as  with  an  atom,  or  atoms, 
belonging  to  the  other  part  of  the  molecule.  Now  oxygen  is 
a  markedly  electro-negative  element ;  from  the  facts  enume- 
rated and  from  other  similar  facts,  the  generalisation  has 
been  made,  that  when  an  atom  of  hydrogen  is  in  direct 
connexion  with  an  atom  of  carbon  which  also  directly  binds 
negative  atoms,  or  negative  groups  of  atoms,  that  hydrogen 
is,  as  a  rule,  'replaceable  by  metal'  &c. ;  i.e.  that  hydrogen 
fulfils  the  function  of  'acidic  hydrogen.'1 

75  In  thus  trying  to  use  the  hypothesis  of  valency  as  a  guide 
towards  determining  the  structures  of  isomeric  molecules,  we 
have  found  it  on  the  whole  advantageous  to  limit  the  appli- 
cation of  this  hypothesis  in  various  ways. 

I.  The  hypothesis  is  applied  in  strictness  only  to  the 
molecules  of  bodies  in  the  gaseous  state. 

II.  The  valency  of  an  atom  of  any  specified  element 
is  defined  as  a  number  which  expresses  the  maximum  number 
of  other  atoms  between  which  and  the  given  atom  there  is 
direct   action    and    reaction   in  a   molecule ;   this  number  is 
determined  by  the  study  of  certain  defined  classes  of  mole- 
cules, viz.  molecules  composed  of  a  single  atom  of  the  specified 
element  combined  with  atoms  of  hydrogen,  fluorine,  chlorine, 
bromine,  or  iodine. 

III.  Isomerism  is  regarded  as  correlated  with  varying 

1  I  am  aware  that  such  expressions  as  are  used  in  these  paragraphs,  '  a  carbon 
atom  is  directly  connected  with,  or  directly  binds  to  itself,  an  atom  of  hydrogen,' 
&c.,  are  very  easily  misunderstood;  they  appear,  at  first  sight,  to  convey  much 
more  precise  information  than  they  really  do  convey.  I  have  more  than  once 
insisted  on  the  importance  of  clearly  remembering  that  these  and  similar  ex- 
pressions are  attempts  to  summarise  facts  concerning  the  reactions  of  compounds 
in  the  language  of  a  special  theory  of  the  structure  of  compounds.  Nor  should 
it  be  forgotten  that,  granting  the  fundamental  hypotheses  of  the  molecular  and 
atomic  theory,  and  also  granting  that  each'  atom  can  directly  interact  with  a 
limited  number  of  other  atoms  in  a  molecule,  we  are  obliged  to  regard  the 
atoms  which  form  any  molecule  as  performing  constant  but  regulated  movements, 
and  not,  as  might  be  supposed  by  a  careless  or  superficial  reader  of  the  atomic 
explanation  of  isomerism,  as  in  absolutely  fixed  positions  within  the  molecule. 


CHAP.  II.  §  75]          STRUCTURAL   FORMULA.  155 

relative  positions  of  the  atoms,  not  with  variations  in  the 
distances  between  identically  arranged  atoms,  forming  a 
molecule. 

IV.  The  atoms  which  form  a  molecule  are  regarded 
as  arranged  in  the  same  plane;  no  attempt  is  made  to  con- 
nect the  facts  of  isomerism  with  the  arrangement  of  the 
atoms  in  different  dimensions  in  space. 

Applying  the  hypothesis  as  thus  limited,  and  for  the  most 
part  to  compounds  of  carbon,  we  found  that  the  structural 
formulae  of  classes  of  carbon  compounds  can  be  general- 
ised so  far  as  to  admit  of  the  assertion  that  the  molecules 
of  the  members  of  any  one  class  are  characterised  by  the 
presence  of  a  special  atomic  group  which  may  be  called  the 
class-group :  and  hence  that  the  first  step  in  assigning  a 
structural  formula  to  a  new  compound  is  to  determine  the 
class  to  which  it  belongs  by  comparing  the  reactions  of 
this  compound  with  those  of  known  substances  belonging 
to  various  classes;  having  done  this,  we  then  eliminate 
from  the  possible  structural  formulae  those  which  do  not 
contain  the  characteristic  group  of  the  class  in  which  our 
compound  is  placed.  Finally,  we  choose  from  the  remaining 
formulae  that  one  which  best  summarises  the  reactions  of  the 
compound  molecule  under  consideration  and  its  relations  to 
other  molecules. 

We  found  that  a  wide  knowledge  of  the  characters  of 
classes  of  compounds  is  required  on  the  part  of  him  who 
would  employ  this  method  with  success,  and  also  that  the 
chemist  has  constantly  to  be  on  his  guard  against  drawing 
too  rigid  conclusions.  A  new  compound  may  represent  a 
new  class,  hence  a  new  class-group  has  to  be  determined  by 
comparing  the  reactions  of  the  new  compound  with  those 
of  others  the  classification  of  which  is  fairly  settled,  and  also 
by  seeking  to  obtain  other  representatives  of  the  new  class. 
The  discovery  and  study  of  new  compounds  apparently 
belonging  to  a  known  class  may  lead  to  a  revision  of  the 
general  formula  assigned  to  the  class,  and  perhaps  to  a 
division  of  the  class  into  sub-classes  each  characterised  by 
its  own  group. 


156  ATOMIC   AND   MOLECULAR   SYSTEMS.         [BOOK  I. 

76  The  application  of  the  hypothesis  of  valency  to  determine 
the  most  probable  of   many  possible  formulae  is  evidently 
a  matter  of  no  little  difficulty.     Certain  generalisations  are 
usually  adopted  as  guides  in  interpreting  the  results  of  the 
study  of  the  chemical  properties  of  molecules.    The  principal 
generalisations  are  these. 

(1)  Those  atoms  which  are  obtained  as  an  undecom- 
posed  group  in   reactions  resulting  in  the  splitting  up  of  a 
compound  are  present  in  the  molecule  of  that  compound  as 
a  group  of  directly  combined  atoms. 

(2)  When   a  group  of  atoms  passes  from  one  com- 
pound molecule  to  another,  the  relative  arrangement  of  these 
atoms,  as  a  rule,  is  not  altered. 

(3)  When  an  atom,  or  group  of  atoms,  replaces  another 
atom  or  group  of  atoms  of  equal  valency  with  itself,  the  re- 
placing atom,  or  group,  occupies  (as  a  rule)  the  same  position 
relatively  to  the  other  atoms  in  the  molecule  as  was  occupied 
by  the  atom,  or  group  of  atoms,  which   it  has  replaced  '  ; 
or  it  may  be  better  to  say,  the  relations  of  the  replacing 
atom,  or  group,  to  the  rest  of  the  molecule  are  generally  the 
same  as  those  of  the  atom,  or  group  of  atoms,  which  it  has 
replaced. 

77  Many  of  the  reactions  given  on  pp.  149  —  154,  as  illus- 
trative of  methods  for  assigning  structural  formulae  to  given 
compounds  also  serve  as  illustrations  of  the  use  of  these 
generalisations  ;  one  or  two  further  illustrations  will  be  given 
here. 

Two  isomerides  each  having  the  composition  C2H6O  are 
theoretically  possible;  viz. 


(i)     H3C  —  C  —  O  —  H        and        (2)     H3C  —  O  —  CH3. 

Two  compounds  having  this  formula  are  known.     One  of 
these  (alcohol)  interacts  with  potassium  or  sodium  thus, 

(a)    C2H6O  +  K  =  C2H5KO  +  H; 
potassium  (or  sodium)  does  not  react  with  the  substance  thus 

1  L.  Meyer,  loc.  cit.  pp.  252  et  seq,  (English  Ed.  pp.  230  —  31)  slightly  modified. 


CHAP.  II.  §§  76,  77]        STRUCTURAL  FORMULA.  1 5  7 

formed :  alcohol  interacts  with  phosphorus  pentachloride 
thus, 

(b)     C2H6O'+  PC15  =  C2H5C1  +  POC13+  HCL 

The  second  isomeride  (methyl  ether)  does  not  interact  with 
potassium  or  sodium  but  reacts  with  phosphorus  penta- 
chloride thus, 

C2H6O  +  PC16=2CH3C1  +  POC13. 

The  first  formula  generalises  the  reactions  of  alcohol,  the 
second  generalises  the  reactions  of  methyl  ether :  thus 

(a)     H3C-CH2-OH  +  K  =  H3C-CH2-OK  +  H; 

one,  and  only  one,  hydrogen  atom  is  represented  in  the 
formula  as  indirectly  bound  (through  an  oxygen  atom)  to 
a  carbon  atom ; 

(ff)     H3C-CH2-OH  +  PC15=H3C-CH2-C1  +  POC13+HC1; 

the  group  OH  is  replaced  by  the  atom  Cl,  which  being  of 
equal  valency  is  regarded  as  occupying  the  place  in  the 
molecule  relatively  to  the  other  atoms  formerly  occupied  by 
the  group  OH. 

The  second  formula  H3C  —  O  —  CH3  assigned  to  methyl 
ether  represents  all  the  hydrogen  atoms  as  directly  reacting 
with  atoms  of  carbon,  it  represents  them  as  having  all  the 
same  function ;  hence  either  none,  or  all,  will  be  replaced  by 
the  action  of  potassium.  But  the  second  formula  represents 
the  atom  of  oxygen  as  in  direct  union  with  atoms  of  carbon 
only ;  if  the  oxygen  atom  should  be  replaced  by  two  mono- 
valent  atoms,  e.g.  by  two  atoms  of  chlorine,  the  molecule 
could  no  longer  hold  together  but  would  separate  into  two 
molecules,  each  having  the  structure  Cl  —  CH3;  this  is  what 
happens  when  methyl  ether  is  acted  on  by  phosphorus  penta- 
chloride. 

When  the  molecule  HO-CH2-CHS  is  oxidised  it  loses 
two  atoms  of  hydrogen,  producing  C2H4O,  which  is  then 
changed,  by  taking  up  one  atom  of  oxygen,  into  the  mono- 
basic acid  C2H4O2.  Probably  the  simplest  way  in  which 
these  changes  can  be  represented  in  structural  formulae  is 


158  ATOMIC   AND    MOLECULAR   SYSTEMS.         [BOOK  I. 

([)     CH3  CH3  (2)     CH3  CH3 

CH2    -    H.,    =    C  C      +  O    =    C  —  O. 

I  I  I  I 

OH  OH  OH  OH 

Now  are  the  properties  of  the  acid  molecule  C2H4O2  such 
as  we  should  expect  if  we  assumed  it  to  have  the  formula 
H3C  —  CO  —  OH  ?  Two  important  reactions  of  the  compound 
in  question  are  these  : — 

(1)  By  reacting  with  phosphorus  pentachloride  it  yields 
C2H3OC1,  and  this  does  not  interact  with  the  same  reagent ; 

(2)  When  the  sodium  salt  of  this  acid  is  heated  with 
caustic  soda  it  is  decomposed  thus, 

C2H3NaO2  +  NaHO=Na2CO3  +  CH4. 

These  reactions  are  expressed  by  the  formula  O  —  C  —  CH3 

I 

OH 

which  is  therefore  adopted  as  the  structural  formula  for  acetic 
acid1. 

Now  let  us  turn  to  the  compound  C2H4O,  intermediate 
between  alcohol  and  acetic  acid.  Is  this  molecule  well  repre- 
sented by  the  formula  H3C  — C  — OH  provisionally  assigned 
to  it?  When  the  compound  in  question  interacts  with  phos- 
phorus pentachloride  it  yields  C2H4C12,  and  not  C2H3C1  as 
might  be  expected  if  the  formula  H3C  —  C  —  OH  were  correct. 
From  synthetical  and  analytical  reactions,  C2H4C12  may  be 
shewn  to  be  best  represented  by  the  structural  formula 
C12  =  CH  — CH3;  assuming  this  formula,  and  remembering 
that  the  reaction  to  be  explained,  viz.  formation  of  C2H4C12 
from  C2H4O,  consists  in  the  replacement  of  one  divalent 
oxygen  atom  by  two  monovalent  chlorine  atoms,  we  apply 
generalisation  (3)  par.  76,  and  conclude  that  the  structure  of 

i  Thus, 
(i)     CH3  CH3  (2)     CH3  CH3 

C— 0  +  PC16   =   C— 0  +  &c.         C— 04-Na-OH   =   H  +  Na2CO3. 

OH  Cl  ONa 

One  of  the  carbon  atoms  in  the  original  molecule  remains  associated  with  3  atoms 
of  hydrogen  throughout  both  processes  of  change,  hence  we  conclude  that  the 
molecule  of  acetic  acid  contains  the  group  CH3. 


CHAP.  II.  §  77]          STRUCTURAL   FORMULA.  159 

the    molecule    C2H4O    is   best    represented    by   the   formula 
0-CH-CH8. 

The  oxidation  of  alcohol  is  then  best  represented  thus  in 
structural  formulae  :  — 

(i)    CH3  CH3  (2)    CH3  CH3 

!  i  I  I 

CH2    -    H2    =    C  —  H  C-H  +  O    =    C  —  OH. 

O  —  H  O  O  O 

Another  and  somewhat  more  complex  illustration,  taken 
from  the  so-called  '  aromatic  '  (or  better  '  benzenoid  ')  carbon 
compounds,  will  serve  to  shew  that  the  generalisations  stated 
in  par.  76,  although  widely  applicable,  must  yet  be  used  with 
great  caution.  Assuming  the  generally  adopted  structural 
formula  for  the  molecule  of  benzene1  (C6H6),  viz.2 

H 

I 

' 


H 

the  existence  of  three,  and  only  three,  isomeric  dichloro-  or 
dibromo-  &c.  benzenes,  becomes  possible,  viz. 

(0  (2)  (3) 

C-C1  C  —  Cl  C  —  Cl 

/\  /  \  /\ 

H  —  C      C  —  Cl  H  —  C      C—  H  H—  C      C  —  H 

H  —  C      C  —  H  H  —  C      C  —  Cl  H  —  C      C  —  H 

\  /  \/  \/ 

C  C  C 

I  I  I 

H  H  Cl 

1  See  Armstrong  and  Groves,  Organic  Chemistry,  pp.  260  —  63;  also  pp.  270— 
74.     See  also  post,  par.  81. 

2  The  fact  that  this  formula  is  generally  used  rather  than  the  more  complex 
formula  originally  proposed  byKekule  with  alternate  'doubly'  and  'singly-linked' 
carbon  atoms,  and  that  most  chemists  are  content  meanwhile  to  overlook  the 
contradiction  involved  in  employing  such  a  formula  and  yet  using  the  language  of 
'  bonds,'  is  indicative  of  the  unsatisfactory  nature  of  this  language  when  rigidly 
applied. 


l6o  ATOMIC   AND   MOLECULAR   SYSTEMS.          [BOOK  I. 

In  (i)  both  chlorine  atoms  are  in  direct  connexion  with 
carbon  atoms  which  are  directly  bound  to  one  another ;  in  (2) 
one  carbon  atom  intervenes,  and  in  (3)  two  carbon  atoms 
intervene,  between  the  atoms  of  carbon  which  directly  interact 
with  the  chlorine  atoms. 

These  three  isomeric  compounds1  are  usually  distinguished 
as  i  :  2,  i  :  3,  and  i  :  4,  dichlorobenzene ;  it  is  evident  that 
1:6=1  :  2,  and  i  :  5  =  i  :  3.  Each  of  these  dichloroben- 
zenes  when  acted  on  by  chlorine  yields  one  or  more  isomeric 
trichlorobenzenes  (C6H3C13).  Korner  has  formulated  a  simple 
method  of  proving  that  I  :  2  dichlorobenzene  can  yield  two, 
i  :  3  can  yield  three,  and  i  :  4  can  yield  only  one,  trichloro- 
benzene2. 

Now  if  the  generalisations  we  are  considering  are  applic- 
able to  the  benzenoid  hydrocarbons,  it  follows  that  any 
di-derivative  of  benzene — C6H4JT2  where  X  is  a  monovalent 
atom  or  group  of  atoms — which,  by  a  simple  series  of  reac- 
tions can  be  obtained  from,  or  can  be  converted  into,  i  :  2 
dichloro-  (or  dibromo-  or  dinitro-)  benzene,  must  be  itself  a 
i  :  2  derivative;  i.e.  the  two  X  groups  or  atoms  must  be  in 
direct  interaction  with  carbon  atoms  between  which  there  is 
direct  mutual  action  within  the  molecule.  A  similar  conclu- 
sion is  drawn  regarding  the  structure  of  those  compounds  of 
the  formula  C8H4JT2  which  can  be  obtained  from  or  reduced 
to  i  :  3,  or  i  :  4,  dichloro  dibromo  or  dinitro-benzene. 

Thus  i  :  3  dinitrobenzene,  by  the  action  of  zinc  and 
hydrochloric  acid,  yields  nitramidobenzene  C6H4NO2NH2; 
by  the  further  action  of  nascent  hydrogen  this  yields 
diamidobenzene  C6H4(NH2)2;  and  diamidobenzene,  by  the 

1  The  carbon  atoms  in  the  hexagon  are  numbered  thus : — 

/c\ 

6  C      C  2 

l(ch 

4 

2  i  :  2  yields  1:2:3,  an^  I  :  a :  4,  ( i  :  2  :  3  =  i  :  2  :  6,  and  i  :  2  :  5  =  i  :  2  :4) 
i  :  3  yields  1:2:3,  and  1:3:4  (which=  i  :  3  :  6), and  1:3:5.    1:4  yields  i    2:4 
{ which  =  1:3:4=1:4:5  =  1:4:6).     See  Armstrong  and  Groves,  loc.  cil.  pp. 
467—8. 


CHAP.  II.  §77]      FORMULAE   OF   BENZENE   COMPOUNDS.  l6l 

'  diazo  reaction'1  (or  'Griess'  reaction'),  yields  bromohydroxy- 
benzene  CeH4Br.  OH;  this  bromohydroxybenzene  is  therefore 
assumed  to  be  a  I  :  3  derivative  of  benzene.  Now  when  this 
body  is  fused  with  caustic  potash  it  yields  one  of  the  three 
isomeric  dihydroxybenzenes  C6H4(OH)2;  in  accordance  with 
generalisation  (3)  par  76  this  dihydroxybenzene  ought  to  be 
regarded  as  a  I  :  3  derivative.  But  I  :  4  bromohydroxy- 
benzene— obtained  by  a  method  similar  to  that  sketched 
above  from  i  :  4  dinitrobenzene — yields,  by  fusion  with 
potash,  the  same  dihydroxybenzene  as  just  mentioned ;  hence 
this  dihydroxybenzene  is  now  shewn  to  be  probably  a  I  :  4 
derivative  of  benzene.  Again,  this  same  dihydroxybenzene 
is  the  sole  product  of  the  fusion  with  potash  at  a  high  tem- 
perature of  i  :  4  iodohydroxybenzene  C6H4I .  OH;  but  when 
this  iodohydroxybenzene  is  fused  with  potash  at  165°  none  of 
the  dihydroxybenzene  already  mentioned  is  obtained  but 
only  one  of  the  dihydroxybenzenes  isomeric  with  it2. 

Another  example,  shewing  how  necessary  it  is  to  apply 
such  generalisations  as  those  under  consideration  only  in  a 
tentative  manner,  is  furnished  by  some  reactions  of  i  :  4 
nitrobromobenzene  C6H4NO2Br.  By  the  action  of  alcoholic 
ammonia  on  this  compound  nitramidobenzene  C6H4NO2NH2 
is  produced ;  that  this  nitramidobenzene  is,  as  we  should 
expect,  a  i  :  4  derivative  of  benzene,  can  be  proved  by  trust- 
worthy evidence.  But  if  the  same  i  :  4  C6H4NO2Br  is  acted 
on  by  potassium  cyanide,  and  the  product  of  this  action, 
C6H4CNBr,  is  boiled  with  dilute  acid,  bromobenzoic  acid, 
C8H4Br(CO2H),  is  obtained,  and  the  reactions  of  this  acid 
prove  beyond  doubt  that  it  is  a  i  :  3,  and  not  as  we  should 
expect  a  1:4,  derivative  of  benzene.  Similarly  the  product 
of  the  action  of  potassium  cyanide  followed  by  that  of  dilute 
acid  on  i  :  3  C6H4NO2Br  is  i  :  2  bromobenzoic  acid, 
C6H4Br  (CO2H),  and  not,  as  a  strict  application  of  the  state- 
ment in  par.  76  would  lead  us  to  expect,  the  i  :  3  derivative. 

1  For  an  account  of  these  '  diazo-reactions,'  which  are  much  used  in  the 
synthesis  of  benzene  derivatives,  see  Armstrong  and  Groves,  loc.  cit.  pp. 
298-9. 

*  See,  for  more  details,  Armstrong  and  Groves,  loc.  cit.  pp.  521—2. 

M.  C.  II 


162  ATOMIC   AND   MOLECULAR   SYSTEMS.          [BOOK  I. 

And  finally,  when  I  :  2  C6H4NO2Br  is  subjected  to  the  action 
of  potassium  cyanide1  no  replacement  of  NO2  by  CN  occurs2. 

78  The  application  of  the  hypothesis  of  valency  to  the  phe- 
nomena of  isomerism  has  rendered  more  definite  that  general 
conception  of  the  molecule  as  a  structure  which  arose  so  soon 
as  it  was  recognised  that  each  atom  in  a  molecule  could  di- 
rectly interact  with  a  limited  number  of  other  atoms.    Analy- 
ses of  reactions,  and  comparisons  of  classes  of  reactions,  have 
led  to  the  adoption  of  certain  rules  which,  when  applied  with 
caution,  have  proved  of  very  considerable  service  in  researches 
on    molecular    structure.     These   researches   have   served    to 
emphasise  the  fundamental  connexion  which  exists  between 
composition  and  properties,  between  function  and  quality  of 
material :  but  chemistry  is  not  now  contented  with  connecting 
the  reactions  of  compounds  with  their  elementary  composi- 
tions, or  even  with  the  atomic  compositions  of  their  molecules, 
she  attempts,  and  is  gradually  succeeding  in  the  attempt,  to 
connect  certain  definite  arrangements  of  atoms  in  molecules 
with  certain  definite  properties  and  actions  of  these  molecules. 

79  In  his  remarkable  paper  published  in  1858,  Kekule  recog- 
nised that  the  function  performed  by  an  atom  in  any  molecule 
depends  on  the  nature  of  the  other  atoms,  as  well  as  on  the 
nature  of  the  given  atom,  and  also  on  the  arrangement  of  all 
the  atoms.     Since    1858    the   nature   of  the  dependence    in 
question   has  been    more  fully  elucidated ;    and  although  it 
cannot  be  said  that  we  have  at  present  much  knowledge, 
capable  of  being  generalised  in  statements  at  once  accurate 
and  wide,  of  the  connexions  between  the  functions  of  parts 
of  molecules  and  the  atomic  compositions  and  structures  of 
these  molecules,  yet  we  are  certainly  gathering  facts  which 
will  doubtless  prove  the  basis  for  far-reaching  generalisations. 

1  In  Armstrong  and  Groves,  loc.  cit.  pp.  334 — 6,  will  be  found  an  account  of 
the  action  of  potassium  cyanide  on  benzene  derivatives ;  this  action,  although 
abnormal,  may  be  expressed  by  a  tolerably  simple  generalisation. 

8  Further  examples  of  the  point  under  discussion  will  be  found  in  the  change  of 
normal  propyl  to  isopropyl,  by  (i)  the  action  of  Al2Br6  [see  Kekule,  Ber.  12.  2279], 
or  (2)  the  action  of  zinc  dust  [see  Jacobsen,  Ber.  12.  1512]:  also  in  the  change  of 
CnH2n+iCN  to  CnH2n+1NC  by  the  action  of  heat :  and  also  in  the  action  of 
reducing  agents  on  phenanthraquinone  (see  Japp,  C.  S.  Journal,  Trans,  for  1883. 
13,  note]. 


CHAP.  II.  §§  78-80]  FUNCTIONS  OF  ATOMS  IN  MOLECULES.    163 

Numerous  illustrations  have  already  been  given  of  the 
existence  of  a  connexion  of  some  kind  between  the  functions 
of  parts  of  a  molecule  and  the  composition,  using  this  term  in 
its  widest  sense,  of  the  whole  molecule.  But  the  existence  of 
such  a  connexion  is  so  important  that  I  shall  devote  a 
paragraph  to  its  illustration. 

The  relation  to  be  illustrated  is  that  between  the  function 
performed  by  an  atom,  or  atomic  group,  in  a  molecule, 


and 


I.     the  nature,  and  arrangement    relatively 
to  the  given  atom  (or  group),  of  the 


other  atoms ; 


otner  atoms ; 
II.  the  general  relative  arrangement  of 


all 


the  parts  ; 


of  the 
mole- 
cule. 


80  I.  That  the  function  performed  by  an  atom  of  hydrogen 
in  a  molecule  varies  according  to  the  nature  and  arrangement 
relatively  to  the  hydrogen  of  the  other  atoms,  has  already 
been  shewn  (see  par.  74,  pp.  151 — 154).  Hydrogen  which  is 
•  associated  with  negative  atoms  or  groups  is  as  a  rule  'replace- 
able by  metals,'  in  other  words,  performs  acidic  functions  in 
the  molecule.  Thus  of  the  two  compounds,  potassium-nitro- 
propane  and  bromonitropropane,  the  latter  is  much  more 
decidedly  acidic  than  the  former :  if  the  formulae  are  com- 
pared, 

K  Br 

H5C2  — C  — NO2  with  H6C2  — C  — NO2, 

I  I 

H  H 

it  is  seen  that,  in  the  markedly  acidic  compound  the  carbon 
atom  with  which  the  sixth  atom  of  hydrogen  is  represented 
as  directly  connected  is  itself  directly  bound  to  the  negative 
group  NO2  and  to  the  negative  atom  Br ;  but  that  in  the  less 
acidic  compound  this  carbon  atom  is  represented  as  directly 
bound  to  the  negative  group  NO2  and  to  the  positive  atom  K. 
Again  C13C  -  H  is  not  an  acid,  but  (NO2)3C  -  H  is ;  the 
influence  of  the  very  negative  NO2  group  seems  to  be  im- 
pressed through  the  carbon  atom  on  the  hydrogen  atom  of 
the  molecule. 


1 64  ATOMIC   AND   MOLECULAR   SYSTEMS.          [BOOK  I. 

In  these  cases  the  atom  of '  acidic  hydrogen '  is  represent- 
ed as  directly  bound  to  a  carbon  atom  within  the  binding- 
sphere  of  which  come  negative  atoms  or  groups.  But  the 
case  of  the  nitrolic  acids,  assuming  the  usually  accepted  for- 
mula (CnH2n+1)— C  -  NO2  to  be  correct,  shews  that 

I 
N-OH 

an  atom  of  hydrogen  which  is  indirectly  bound  to  carbon 
itself  binding  negative  groups  may  react  as  acidic  hydrogen. 
Glyoxaline  and  tribromoglyoxaline  also  furnish  examples 
in  point;  each  of  these  molecules  contains  one  atom  of  acidic 
hydrogen1. 

A  portion  of  the  hydrogen  in  monohydric  alcohols  is  re- 
placeable by  metal,  but  only  by  the  very  positive  metals ;  e.g. 
C2H5.OH  +  K  =  C2H5OK+H;  but  by  the  introduction  of 
an  atom  of  sulphur  into  the  molecule  in  place  of  oxygen  a 
thio-alcohol  is  obtained  which  readily  exchanges  hydrogen 
even  for  comparatively  negative  metals2,  e.g. 

2C2H5SH  +  HgO  =  (C2HsS)2Hg  +  H2O. 

Again,  the  experiments  of  R.  Meyer  appear  to  prove  that  an  atom  of 
hydrogen  in  the  molecule  of  a  carbon  compound  can  be  replaced  by  the 
group  OH,  by  the  action  of  oxidising  agents,  only  when  the  carbon  atom 
with  which  the  hydrogen  is  directly  connected  does  not  directly  bind  any 
other  hydrogen  atoms;  thus  isobutyric  acid  is  oxidised  by  potassium 
permanganate  to  isohydroxybutyric  acid,  but  normal  butyric  acid  yields 
acetic,  oxalic,  carbonic,  and  other  acids,  under  the  same  conditions. 

O 
[In  structural  formulae ;  H3C  —  CH2  —  CH2  —  C^         does  not  yield 

OH 

O^  ^CH3  O^  XCH3 

a  hydroxy-acid ;  but  C  —  CH          yields  C  — COH      .] 

HO^  XCH3  '  HO/  XCH3 

1  The  most  probable  formulae  are, 

CH  — CH— CH— NH  CBr— CBr— CBr— NH 

\N/  \N/ 

(see  Armstrong  and  Groves,  loc.  cit,  p.  769).  Some  reactions  of  water  are  con- 
sistent with  the  statement  that  one  of  the  hydrogen  atoms  performs  the  functions 
of  acidic  hydrogen ;  e.g. 

HOH  +  CH3ONa  =  CH3OH  +  NaOH. 

2  For  details  concerning  these  reactions  see  Armstrong  and  Groves,  loc.  cit., 
pp.  660 — i. 


CHAP.  II.  §8 1]    FUNCTIONS   OF   ATOMS   IN   MOLECULES.        165 

81  II.  A  good  illustration  of  the  influence  exerted  by  the 
arrangement  of  all  the  atoms  in  a  molecule  on  the  functions 
of  one,  or  some,  of  these  atoms,  is  afforded  by  a  comparative 
study  of  the  two  groups  of  carbon  compounds,  more  especially 
the  hydrocarbons,  generally  known  as  'fatty'  (or  'paraffinoid') 
and  'aromatic'  (or  'benzenoid')  respectively1:  a  few,  but  only 
a  few,  of  the  more  important  points  will  be  briefly  stated. 

Comparing  the  interaction  between  concentrated  nitric 
or  sulphuric  acid  and  a  paraffin,  e.g.  C2H6,  with  the  inter- 
action of  the  same  acid  with  a  benzene,  e.g.  C6H6 ,  it  is 
noticed  that  while  one  or  more  hydrogen  atoms  in  the 
molecule  of  the  latter  are  readily  replaced  by  the  groups  NO2 
or  SO8H,  the  acids  are  without  action  on  the  former  hydro- 
carbon. When  the  homologues  of  benzene  are  oxidised,  they 
generally  yield  quinones,  the  molecule  of  any  one  of  which 
contains  the  same  number  of  carbon  atoms  as  the  parent 
hydrocarbon  but  has  two  atoms  of  oxygen  in  place  of  two 
atoms  of  hydrogen  in  the  original  molecule.  When  the 
paraffinoid  hydrocarbons  on  the  other  hand  are  oxidised 
they  do  not  yield  derivatives  analogous  to  the  quinones, 
but  rather  afford  mixtures  of  acids  the  molecule  of  each  of 
which  contains  fewer  carbon  atoms  than  were  present  in  the 
original  hydrocarbon  molecule. 

When  chlorine  reacts  with  the  molecule  of  a  paraffinoid 
hydrocarbon  containing  only  tetravalent8  carbon  atoms  it 
produces  chloro-substitution  derivatives  containing  tetravalent 
carbon  atoms,  the  whole  of  the  hydrogen  in  the  hydrocarbon 
being  eventually  replaced  by  chlorine  ;  the  further  action  of 
chlorine  then  frequently  results  in  a  separation  of  the  mole- 
cule into  two  or  more  molecules,  each  containing  a  smaller 
number  of  carbon  atoms  than  the  original  molecule.  When 
however  chlorine  reacts  with  the  molecule  of  a  paraffinoid 
hydrocarbon  containing  two  or  more  trivalent 3  carbon  atoms 
it  generally  combines  with  it  and  so  produces  a  molecule 
containing  tetravalent  carbon  atoms,  which  then  reacts  with 

1  See  Armstrong  and  Groves,  loc.  cit.  pp.  391 — 402. 

2  In  ordinary  nomenclature  it  would  be  said  '  singly-linked  carbon  atoms." 

3  In  ordinary  nomenclature  it  would  be  said  '  doubly-linked  carbon  atoms.' 


1 66  ATOMIC   AND   MOLECULAR   SYSTEMS.          [BOOK  I. 

chlorine  as  hydrocarbons  with  tetravalent  carbon  atoms 
usually  do.  Thus  when  propane,  H3C  — CH2  — CH3,  reacts 
with  chlorine,  chloro  -  derivatives  H3C  -  CH2  -  CH2C1, 
H3C  —  CH2  —  CHC12,  &c.  and  finally  octochloropropane 
C13C  —  CC12  —  CC13,  are  produced  ;  and  when  this  octo- 
chloropropane is  caused  to  interact  with  iodine  chloride, 
two  compounds,  viz.  C13C  — CC13  and  CC14,  are  formed.  On 
the  other  hand  when  propylene,  H2C  — CH2  — CH2,  the 
molecule  of  which  contains  two  trivalent  atoms  of  carbon, 
reacts  with  chlorine  propylene  chloride,  C1H2C-CH8-CH2C1, 
is  produced  ;  and  this  compound,  which  contains  only  te- 
travalent carbon  atoms  in  its  molecule,  is  decomposed  by 
the  action  of  iodine  chloride,  first  into  C3C18,  and  then  into 
C2C16  and  CC14. 

The  interaction  of  chlorine  with  the  hydrocarbon  benzene, 
C6H6,  finally  results  in  the  formation  of  hexachloro-benzene 
C6C16,  in  which,  it  may  be  safely  asserted  from  the  formula 
and  from  a  study  of  the  properties  of  the  compound,  the 
carbon  atoms  directly  interact  with  the  same  number  of 
atoms  as  in  the  original  C6H6  molecule.  So  far  then  benzene 
behaves  like  a  paraffin:  but  IC1  has  no  action  on  C6C16;  the 
molecule  refuses  to  separate  into  parts  ;  the  six  atoms  of 
carbon  are  apparently  more  firmly  joined  together,  and  form 
a  more  stable  group,  than  the  carbon  atoms  in  the  molecule 
of  a  paraffin. 

The  functions  both  of  the  hydrogen  and  the  carbon  atoms 
in  the  molecules  of  a  benzene  and  of  a  paraffin — say  in  C6H6 
and  in  C6HU — evidently  depend  to  some  extent  on  the  general 
arrangement  of  all  the  atoms  in  these  molecules. 

The  arrangement  of  carbon  atoms  supposed  to  characterise 
the  molecule  of  a  fatty  hydrocarbon,  e.g.  a  paraffin,  is  usually 
spoken  of  as  an  arrangement  in  'an  open  chain?  while  that 
supposed  to  characterise  the  molecule  of  an  aromatic  hydro- 
carbon, e.g.  a  benzene,  is  called  'a  closed  ring.'1  If  the  inter- 

1  Ring-formed  molecules  resemble .  unsaturated  molecules  in  that  they  can 
directly  combine  with  monovalent  atoms  without  loss  of  any  of  their  constituent 
atoms,  e.g.  benzene  forms  C6H6C16 ;  but  they  resemble  saturated  molecules  in 
that  the  assumption  of  monovalent  atoms  is  possible  only  when  preceded  by 


CHAP.'II.§8l]    FUNCTIONS   OF   ATOMS   IN   MOLECULES.        l6/ 

action  between  atom  and  atom  be  supposed  to  begin  at  one 
of  the  carbon  atoms,  then  in  a  closed  ring  molecule  it  returns 
to  that  atom ;  in  other  words  each  carbon  atom  acts  on,  and 
is  acted  on  by,  at  least  two  other  carbon  atoms  in  the 
molecule :  but  in  an  open  chain  molecule  the  action  does  not 
return  to  the  carbon  atom  at  which  it  started  ;  in  other  words, 
there  are  two  carbon  atoms  in  the  molecule,  each  of  which 
acts  on,  and  is  acted  on  by,  only  one  other  carbon  atom. 

The  ring-formed  molecule  containing  six  carbon  atoms 
may  be  represented  thus  : — 

C 

/  \ 

C  — C  — C  or  thus  C      C 

II  I        I 

C— C— C  C      C 

v/ 

C 

and  the  open  chain  molecule  thus  : — 

C  — C  — C  — C-C  — C. 

As  the  six  carbon  atoms  in  the  molecule  of  benzene  ap- 
pear to  form  a  very  stable  group,  they  are  sometimes  spoken 
of  as  the  '  six-carbon-nucleus'  of  the  molecule.  Now  if  the 
monochloro-derivative  of  xylene,  C8H10,  produced  by  the 
reaction  of  chlorine  with  that  hydrocarbon  when  cold  is 
compared  with  the  monochloro-derivative  produced  by  the 
reaction  of  chlorine  with  the  same  hydrocarbon  when  hot, 
it  is  found  that  the  latter  readily  exchanges  its  chlorine  atom 
for  the  group  OH  with  production  of  an  alcohol,  C8H9(OH), 
but  that  the  chlorine  atom  in  the  former  can  scarcely  be 
replaced  by  other  radicles.  If  we  assume  the  ordinarily 
accepted  structural  formulae  for  the  two  isomeric  mono- 
chloroxylenes  we  at  once  see  how  profoundly  the  functions 

a  redistribution  of  the  mutual  actions  between  some  of  the  polyvalent  atoms. 
(Lossen.) 

The  number  of  molecules  produced  in  any  reaction  wherein  only  saturated 
molecules  take  part  is  equal  to  or  greater  than  the  number  of  molecules  taking 
part  in  the  reaction  :  when  the  number  produced  in  any  reaction  is  smaller  than 
the  number  of  molecules  originally  taking  part  in  the  reaction,  at  least  one  of  the 
reacting  molecules  must  be  either  unsaturated  or  ring-formed.  (Lossen.) 

It  is  evident  that  a  ring-formed  molecule  must  contain  at  least  three  polyvalent 
atoms,  and  that  for  such  molecules  «j  <  «3+  2«4  +  &c....  +  2. 


168  ATOMIC   AND   MOLECULAR   SYSTEMS.          [BOOK  I. 

of  the  chlorine  atoms  depend  on  the  relative  arrangement  of 
all  the  atoms  in  the  molecule.     The  formulae  in  question  are 

(a)  monochloroxylene  from  hot  xylene 

H         H2 

/c\       II 
HC       C  —  C  —  CH2C1, 

I         I 
HC       CH 

^C^ 
H 

(b]  monochloroxylene  from  cold  xylene 

HC  H2 

/  \         II 
HC       C  —  C  —  CH3. 

HC       C  —  Cl 
\  / 
CH 

The  chlorine  atom  in  (a)  is  said  to  be  in  '  the  side  chainl 
and  in  (b)  in  the  ''central  nucleus!  In  the  hydrocarbon  C8H10 
we  have  the  properties  both  of  a  paraffin  and  a  benzene  ;  part 
of  the  molecule,  the  six-carbon-nucleus,  behaves  as  a  ben- 
zenoid  group  ;  the  other  part,  the  side  chain  C2H5,  as  a  paraffi- 
noid  group. 

A  comparison  of  some  of  the  reactions  of  metallic  hy- 
droxides, alcohols,  and  phenols,  will  serve  to  illustrate  the 
dependence  of  the  functions  of  part  of  a  molecule  at  once  on 
the  nature,  and  arrangement  relatively  to  this  part,  of  the 
other  atoms,  and  also  on  the  general  arrangement  of  all  the 
atoms,  in  the  molecule. 

The  interactions  of  acids  with  metallic  hydroxides  and 
alcohols  result  in  the  formation  of  salts  :  — 
Zn(OH)2+2HCl  =  Zn 


But  phenols  do  not  yield  analogous  products  by  their  reactions 
with  acids.  Alcohols  and  some  metallic  hydroxides,  e.g. 
Zn(OH)aand  Al2(OH)a,  yield  unstable  metallic  derivatives  by 
reacting  with  markedly  positive  metals  or  their  hydroxides  ; 
phenols  however  yield  much  more  stable  metallic  derivatives 
by  reacting  with  the  same  metals,  or  their  hydroxides.  The 
hydrogen  atom  (or  atoms)  which  is  indirectly  connected, 


CHAP.  II.  §8l]    FUNCTIONS   OF   ATOMS   IN   MOLECULES.        169 

through  oxygen,  with  the  metal  or  hydrocarbon-radicle  of 
the  molecules  of  alcohols,  certain  metallic  hydroxides,  and 
phenols  evidently  fulfils  more  or  less  acidic  or  basic  functions 
according  to  the  nature  of  the  other  part  of  the  molecule. 
When  that  other  part  is  a  strongly  positive  metallic  atom  (or 
atoms)  the  hydrogen  is  basic;  when  the  metallic  atom  (or 
atoms)  is  not  markedly  positive  the  hydrogen  as  a  rule  is  at 
once  basic  and  acidic  in  function ;  when  the  nonhydroxylic 
part  of  the  molecule  is  composed  of  carbon  and  hydrogen 
atoms  arranged  in  an  '  open  chain '  the  hydrogen  appears  to 
be  more  or  less  analogous  to  the  hydrogen  of  metallic  hy- 
droxides; and  when  the  carbon  and  hydrogen  of  the  nonhy- 
droxylic part  of  the  molecule  are  arranged  in  a  '  closed  ring ' 
the  hydrogen  appears  to  be  more  distinctly  acidic  in  function  1. 

The  following  facts  and  generalisations  concerning  the 
action  of  reagents  on  various  benzene  derivatives  afford  further 
examples  of  the  influence  exerted  by  the  relative  position, 
and  nature  of  the  parts,  of  a  molecule,  and  the  general  ar- 
rangement of  all  the  atoms  in  a  molecule,  on  reactions  wherein 
atoms,  or  atomic  groups,  in  the  molecule  are  substituted  by 
other  atoms  or  groups. 

In  the  production  of  certain  di-substituted  derivatives  of 
benzene  C6H4JTJr',  from  mono- substituted  derivatives  C6H5^f, 
it  is  found  that  whether  the  di-derivative  shall  belong  to  the 
i  :  2,  I  :  3,  or  i  :  4  series2,  depends  on  the  nature  of  the  atom 
or  atomic  group  X  in  C6H6Jf,  and  also  on  the  nature  of  the 
atom  or  group  X'  in  C6H4XX'.  When  X  =  Cl,  Br,  I,  OH, 
CH3,  CH.C1,  CHC12,  CC13,  or  NH2,  and  X'  =  C\,  Br,  I,  NO2, 
or  SO3H,  the  di-derivative  CeHtXX'  generally  belongs  to  the 
i  :4  series:  when  ^=NO2,SO3H,  CN,  CHO,  COCH3,  or 
CO2H,  and  X1  =Cl,  Br,  I,  NO2,  or  SO3H,  then  C6H<XX' 
generally  belongs  to  the  i  :  3  series8. 

When  derivatives  of  benzene  containing  paraffinoid  radicles 
as  '  side  chains '  are  oxidised  they  yield  mono-,  di-,  tri-,  &c., 

1  See  Armstrong  and  Groves,  loc.  dt.  p.  566. 

2  See  par.  77,  p.  160,  for  an  explanation  of  this  notation. 

3  See  table  in  Armstrong  and  Groves,  loc.  cit.  p.  337 :  also  Armstrong,  C.  S. 
Journal,  Trans,  for  1887.  258. 


I/O  ATOMIC   AND   MOLECULAR   SYSTEMS.          [BOOK  I. 

basic  acids,  according  to  the  number  of  side  chains  in  the 
original  molecule;  thus  C6H4.C2H5.CH3  yields  C6H/CO2H)2, 
C6H4.CH,.C02H  also  yields  C6H4  (CO2H)2,  &c.:  but  if  a 
negative  atom  or  group  is  introduced  into  the  benzene  deri- 
vative and  the  oxidation  is  then  effected,  the  paraffin-radicle 
which  forms  the  side  chain  nearest  to1  the  negative  atom  (or 
group)  is  protected  by  that  atom  (or  group)  and  does  not  un- 
dergo oxidation.  Thus  C6H4.CH3.C2H5  [1:4]  when  oxidised 
produces  C6H4(CO2H)2;  but  C6H3.Br.CH3.C2H5  [i  :  2  -.4]  pro- 
duces C6H3Br.CH3.CO2H  [1:2:  4].  So  again  C6H4(C2H5)2 
[i  :  4]  oxidises  to  C6H4(CO2H)2 ;  but  C6H3.C2H8.SO2NH2.C2H5 
[1:2:4]  oxidises  to  C6H3.C2H5.S02NH2.CO2H  [1:2:4];  in  the 
latter  case2  the  C2H5  nearest  to  the  negative  group  is  protected, 
while  the  other  C2H5  group  undergoes  oxidation  to  CCXH. 
So  also  if  i  :  3  :  4,  i  :  4  :  5,  or  i  :  2  :  4,  dimethylnitroxylene 
(C8H7.CH3.CH3.NO2)  is  oxidised,  in  each  case  the  CH3  group 
nearest  to  the  NO2  group  is  unchanged,  and  the  other  CH3 
group  is  oxidised  to  CO2H  ;  but  if  1:3:5  dimethylnitro- 
xylene is  oxidised,  both  the  CH3  groups  are  converted  into 
CO2H  groups :  now  in  a  1:3:5  derivative  the  substituting 
groups  are  equally  distributed  ;  in  the  case  before  us  each 
methyl  group  is  situated  in  exactly  the  same  position  relatively 
to  the  NO2  group3. 

1  'Nearest  to':  compare  the  structural  formulae  for  the  three  methylbromo- 
benzenes 

CH3  CH3  CH3 


C] 

0 


* 


Br 
1:2  1:3  1:4 

the  Br  atom  is  said  to  be  nearer  to  the  CH3  group  in  the  i  :  i  than  in  the  i  :  3, 
and  nearer  in  the  i  :  3  than  in  the  i  :  4  compound. 

2  See  Remsen  and  Hall,  Amer.  Chem.  yournal  2.  50 ;  and  Remsen  and  Noyes, 
ibid.  4.    197. 

3  See  E.  Wroblewsky,  £er.  15.  1021.     Compare  the  following  formulae  where 
X  represents  the  group  CH3  and  A  the  group  NO2: — 


SL  .A. 

0'       .0: 


CHAP.  II.  §§8 1,  82]        MOLECULAR   STRUCTURE.  I/ 1 

Again,  when  thiophene,  C4H4S,  is  acted  on  by  nitric  acid 
the  thiophene  is  completely  oxidised  ;  but  when  negative 
groups  are  introduced  into  the  thiophene  molecule  the  pro- 
ducts react  with  strong  nitric  acid  to  produce  nitro-derivatives1. 
Thus  moniodothiophene,  C4H3IS,  yields  nitriodothiophene 
C4H2I(NO.2)S  ;  and  dibromothiophene,  C4H2Br2S,  yields  dini- 
trodibromothiophene,  C4Br.,(NO2)2S. 

:  From  these  considerations  it  would  appear  that  the 
readiness  to  undergo  this  reaction  or  that,  or,  as  might  be 
said,  the  chemical  stability  of  a  molecule,  depends  largely 
on  the  balance  of  properties  of  the  parts  of  the  molecule,  such 
balance  being  itself  connected  with  the  nature  and  relative 
arrangements  of  these  parts.  Many  of  the  reactions  cited 
in  the  foregoing  paragraphs  (80  and  81)  may  serve  as 
illustrations  of  the  meaning  of  the  expression  '  chemical 
stability',  and  of  the  conception  of  a  dependence  between  this 
and  the  balance  of  functions  of  parts  of  the  molecule  ;  let 
one  more  illustration  suffice. 

The  conditions  under  which  an  atom  of  hydrogen  ap- 
parently fulfils  alcoholic  functions  have  been  already  sum- 
marised [pp.  168 — 169].  In  some  molecules  the  acid  and 
alcoholic  functions  of  the  hydrogen  atoms  seem  to  be  equally 
balanced,  so  that  for  some  purposes  the  compound  may  be 
classed  as  an  alcohol,  for  other  purposes  as  an  acid ;  thus,  when 
an  atom  of  hydrogen  in  the  benzene  molecule  is  replaced 
by  the  group  OH,  the  product,  phenol  C6H5.OH,  exhibits 
some  of  the  properties  of  an  acid  and  also  some  of  the 
properties  of  an  alcohol;  e.g.  an  atom  of  hydrogen  is 
replaceable  by  metal  when  the  compound  is  acted  on  by 
an  alkali  metal  or  alkaline  hydroxide,  but  not  when  it  is 
acted  on  by  an  alkaline  carbonate2.  By  replacing  three 
hydrogen  atoms  in  the  phenol  molecule,  C6H5  .  OH,  by 
NH2  and  NOS  groups,  compounds  are  obtained  which  ex- 
hibit both  basic  and  acidic  properties;  e.g.  the  molecule 


1  H.  Kreis,  Ber.  17.  2073. 

2  In  these  actions  phenol  presents  an  analogy  to  aluminium  hydroxide- 

Ala  (OH)8. 


172  ATOMIC   AND   MOLECULAR   SYSTEMS.          [BOOK  I. 

C6H2  .  (NH2)  .  (NO2)2  .  OH  combines  with  HC1,  but  the 
product  is  not  very  stable ;  the  same  molecule  however  readily 
exchanges  an  atom  of  hydrogen  for  metal  by  the  action  of 
alkaline  carbonates,  thus  forming  well-marked  stable  metallic 
derivatives,  e.g.  C6H2(NH2)(NO2)2ONa.  If  however  two  NH2 
groups  and  one  NO2  group  are  introduced  in  place  of 
three  hydrogen  atoms  in  the  phenol  molecule,  the  product 
C6H2(NH2)2(NO,)OH  is  distinctly  basic,  combining  readily 
with  HC1,  but  yielding  only  unstable  metallic  derivatives. 

83  Not  only  is  the  general  chemical  stability  of  a  molecule 
dependent,  in  part,  on  the  balance  of  functions  of  the  atoms 
and    atomic    groups    in    the    molecule,    but    many   of    the 
properties   generally  called    physical   are    correlated  with  a 
similar  balance  of  parts.     Thus  Witt l  has  shewn  that  there 
exists   a   definite  connexion  between   the  tinctorial  proper- 
ties  of  many   derivatives    of  azobenzene,    C6H5  —  N2  —  C6H5, 
and   the  atomic   composition  and   structure   of  these  mole- 
cules.    By  introducing  the  group  NH2  in  place  of  hydrogen 
in    the    azobenzene    molecule    salt-forming    molecules    are 
produced,   possessed   of   considerable   dyeing   properties;    if 
negative    groups,   as    OH,  HSO3,  &c.    are    introduced    into 
the    molecule    the    products    are    also    strongly    coloured ; 
but  the  best   dyes   are   formed    by   compounds    which    are 
neither  markedly  basic  or  acidic.    Thus  C6HS-  N2  -  C6H4(NH2) 
dyes    a    light    yellow,    but    the    colour    is     very    fugitive; 
the    colour    of    (NH2)C6H4  -  N2- C6H3(NH2)2    is    too    dull; 
but   when    an  azotised  or   a   di-azotised    base   is   combined 
with   a   negative   phenolic  or   naphtholic   group,  good  dyes 
are  usually  obtained;  e.g.  C6H6  -  N2-C10H5(SO3H)(OH)  or 
C6H5  -  N2  -  C6H4  -  N,  -  C6H4O  H. 

84  We  have  already  learned  (pars.   32 — 34)  that  a  general 
relation  exists  between  the  crystalline  form  of  a  compound 
and  the  number  and  arrangement  of  the  atoms  in  the  molecule 
of  that  compound.     Groth2,  and  others,  have  shewn  that  the 

1  C.  S.  Journal,  Trans,  for  1879.  179  and  357 :  also  Hartley,  C.  S.  Journal, 
Trans,  for  1887.  152. 

"  P°gg-  Ann.  141.  31.  See  also  C.  Hintze,  Pogg.  Ann.  ErgzM.  6.  195; 
C.  Bodewig,  Pogg.  Ann.  158.  239;  P.  Friedlander,  Zeitschr.  Krystall.  3.  168; 


CHAP.  II.  §§  83,  84]        MORPHOTROPIC   RELATIONS.  173 

substitution  of  Cl,  Br,  NO2,  or  OH  &c.,  for  hydrogen  in  the 
molecules  of  benzene  derivatives  is  accompanied  by  definite 
changes  in  the  crystalline  forms  of  the  compounds.  The 
relations  existing  between  crystalline  form  and  chemical 
structure,  so  far  as  the  latter  is  modified  by  processes  of 
substitution,  are  called  by  Groth  morphotropic  relations.  The 
change  of  crystalline  form  in  any  given  case  depends  on 
(i)  the  chemical  nature  of  the  parent  substance;  (2)  the 
crystalline  system  to  which  it  belongs ;  (3)  the  chemical  nature 
of  the  substituting  atom  (or  group);  and  (4)  the  chemical 
nature  of  the  product  of  the  reaction,  using  the  expression 
'  chemical  nature'  in  its  widest  sense  as  including  the  con- 
ceptions of  atomic  composition  and  atomic  structure. 

When  the  parent  substance  belongs  to  a  crystalline  system 
in  which  the  relations  of  the  axes  are  not  invariable,  substitu- 
tion of  Cl,  Br,  &c.,  generally  only  produces  changes  in  these 
relations,  without  total  changes  to  other  systems ;  but  if  the 
parent  substance  belongs  to  the  regular  system,  the  substituted 
product  is  found  to  belong  to  one  of  the  other  five  systems. 

Groth's  researches  lead  to  the  following  generalisations 
concerning  the  derivatives  of  benzene  : — 

(1)  Substitution  of  H  by  OH  or  NO2,  is  accompanied 
by  changes  in  the  relations  of  the  axes,  but  not  by  changes 
from  one  system  to  another. 

(2)  Substitution  of  H  by  Cl  or  Br,  is  accompanied  by 
changes  from  one  crystalline  system  to  another,  less  sym- 
metrical, system;  but  further  substitution  by  the  same  atoms  is 
sometimes  accompanied  by  a  return  to  a  more  symmetrical 
system. 

(3)  Substitution  of  H  by  CH3  is  also  accompanied  by 
marked  changes  in  crystalline  symmetry. 

(4)  Chemically  similar  derivatives  of  benzene  belonging 
to  zpara  [i  :  4]  series  shew  greater  crystallographic  analogies 
with  one  another  than  with  the  members  of  a  meta  [i  13]  or 
an  ortlw  [1:2]  series. 

and  the  article  '  Isomorphie '  in  the  Nates  Handivorterbwh  dcr  Chemie,  3.  especially 
pp.  854 — 9;  also  'Isomorphie'  in  Ladenburg's  Handworterbzich  der  Chemie,  5. 
pp.  401—5. 


174  ATOMIC   AND    MOLECULAR   SYSTEMS.          [BOOK  I. 

The  general  conclusion  to  be  drawn  from  these  facts  is, 
that,  in  some  compounds  at  any  rate,  crystalline  form  is 
more  or  less  closely  connected  with  the  nature  and  arrange- 
ment, as  well  as  with  the  number,  of  the  atoms  and  groups  of 
atoms  in  the  compound  molecules. 

85  Very     many    measurements     have    been    made    of    the 
quantities  of  heat  which  are  produced  or  disappear  during 
processes  of  chemical    change.     This   subject   will   be   con- 
sidered more  fully  in  a  future  chapter1;  at  present  I  wish  to 
insist  on  the  fact  that  the  data  of  thermal  chemistry  establish 
an  undoubted  connexion  between  the  thermal  changes  which 
accompany  chemical  reactions  and  the  nature  and  arrange- 
ment  of    the   atoms,    and    groups    of    atoms,    forming    the 
molecules   which    take    part    in    these   reactions.     Especial 
reference    must    be    made   here    to   the   experiments   of    J. 
Thomsen2,   from  which   the  conclusion  can   be   drawn    that 
the  change  from  a  material  system  of  isolated  atoms — say 
x  carbon  atoms,  x1  hydrogen  atoms,  and  x"  oxygen  atoms — 
to  a  molecular  system  in  which  these  atoms  are  combined  so 
that  all  the  carbon  atoms  are  tetravalent  (i.e.  each  acts  on 
and  is  acted  on  by  four  other  atoms)  and  all  the   oxygen 
atoms  are  divalent,  is  attended  with  the  loss  to  the  system  of 
a  quantity  of  energy  different  from  that  which  accompanies 
the  change  from  the  same  system  of  isolated   atoms   to   a 
molecular  system  in  which  some,  say  (x-2],  carbon  atoms 
are    trivalent,   and    some,   say    (x"  —  i),    oxygen   atoms   are 
monovalent. 

86  The  measurements  which  have  been  made  of  the  quantities 
of  heat  that  are  produced  or  disappear  during  similar  chemical 
changes  undergone  by  isomeric  compounds  shew  that  in  many 
cases  at  any  rate  the  quantity  of  energy  associated  with  one 
isomeride    is   different   from   that   associated   with   another. 
Thus,  the  heat  produced   during   the   complete  combustion 
of  dipropargyl  (C6H6)  is  about  850,000  gram-units,  while  that 
produced  during  the  combustion  of  the  isomeric  molecule 

1  See  Chapter  iv.  Section  i. 

2  Ber.  13.  1321  ;  Journal fiir prakt.  Chemie.  23.  157  and  163  ;  and  Zeitschr.  f, 
physikal.  Chemie.  1,  369.     See  also/w/,  chap,  iv.,  par.  134. 


CHAP.  II.  §§85-87]     THERMAL   WORK   ON    TSOMERISM.  175 

benzene  is  about  800,000  gram-units  ;  hence  the  amount  of 
energy  associated  with  the  arrangement  of  six  atoms  of 
carbon  and  six  atoms  of  hydrogen  in  the  molecule  of 
benzene  is  less  than  that  associated  with  the  arrangement 
of  the  same  numbers  of  the  same  atoms  in  the  molecule 
of  dipropargyl.  But  in  the  molecule  of  benzene  each  carbon 
atom  is  at  least  trivalent  (and  possibly  tetravalent),  while  in 
that  of  dipropargyl  some  of  the  carbon  atoms  are  certainly 
divalent1:  hence,  it  might  apparently  be  concluded,  that  more 
energy  is  degraded  in  the  formation,  from  atoms  of  carbon  and 
hydrogen,  of  a  molecule  in  which  all  the  carbon  atoms  act  as 
tri-  or  tetravalent  atoms,  than  of  an  isomeric  molecule  in 
which  some  of  the  carbons  act  as  divalent  atoms.  But  it 
must  be  remembered  that  in  the  benzene  molecule  each 
carbon  atom  directly  interacts  with  not  more  than  one  atom 
of  hydrogen,  and  with  at  least  two  other  atoms  of  carbon ; 
whereas  in  the  molecule  of  dipropargyl  it  is  very  probable 
that  two  of  the  carbon  atoms  directly  interact  each  with  a 
single  other  carbon  atom,  and  also  that  some  of  the  atoms 
of  carbon  interact  each  with  two  atoms  of  hydrogen.  Hence, 
if  we  may  provisionally  draw  a  general  conclusion  from  the 
very  limited  data  before  us,  it  might  be  inferred  that  the 
differences  between  the  quantities  of  energy  associated  with 
different  isomeric  atomic  systems  depend,  among  other  con- 
ditions, on 

(1)  whether    each    atom    directly    interacts    with    the 

maximum  number  of  other  atoms;  in  other 
words,  on  the  actual  valencies  of  the  atoms  in 
the  molecules ;  and 

(2)  on  the  nature   of  the  atoms  between  which  direct 

interaction  occurs ;  in  other  words,  on  the  dis- 
tribution of  the  interatomic  reactions. 

87        The  following  data,  in  addition   to  the  numbers  already 
given    for  the  heats   of  combustion   of  benzene  and   dipro- 

1  The  usually  adopted  formula  for  the  dipropargyl  molecule  is 

HC— C— CHa— CH2— C— CH, 
which  contains  2  tetra-  and  4  divalent  carbon  atoms. 


176  ATOMIC   AND   MOLECULAR   SYSTEMS.          [BOOK  I. 

pargyl,  serve  to  illustrate  the  existence  of  a  relation  between 
the  quantities  of  energy,  and  the  valencies  of  the  atoms,  in 
isomeric  molecules. 


Empirical  formula 
C3H60 


(i)     propaldehyde 


Heat  of  combustion. 

420,000  gram-units. 


H,C  — CH,— c; 


(2)     allylalcohol  442,000  gram-units. 

H2C— CH— CH2— OH 

Assuming  the  correctness  of  these  structural  formulae,  it 
is  seen  that  the  propaldehyde  molecule  contains  two  tetra- 
and  one  trivalent  carbon  atoms,  and  also  one  monovalent 
oxygen  atom,  whereas  the  molecule  of  allylic  alcohol  con- 
tains two  tri-  and  one  tetravalent  carbon  atoms,  and  also  one 
divalent  oxygen  atom. 

88  The  data  of  thermal  chemistry  furnish  more  numerous 
examples  of  the  existence  of  a  connexion  between  greater 
or  less  molecular  energy  and  the  distribution  of  the  atomic 
interactions  in  isomeric  molecules. 


Empirical  formula 
C3H602 


(i)  ethyl  formate 


H/ 

(2)  methyl  acetate 
C> 


H, 


—  C2H, 


— O  — CH. 


Heat  of  combustion. 

390,000  gram-units. 


395,000  gram-units. 


If  the  structural  formulae  given  are  correct,  then  in  each 
of  these  molecules  we  have  two  tetra-  and  one  trivalent 
carbon  atoms,  and  one  mono-  and  one  divalent  oxygen 
atoms;  but  the  trivalent  carbon  atom  in  ethyl  formate  inter- 
acts directly  with  two  oxygen  and  one  hydrogen  atoms,  and 
in  methyl  acetate  with  two  oxygen  and  one  carbon  atoms :  in- 
spection of  the  formulas  will  disclose  other  differences  in  the 
distribution  of  the  atomic  interactions. 

Alcohol  and  methylic  oxide  afford  another  example  of  the 
relation  we  are  discussing  : — 


I. 

Empirical  formula 
C3H00 


CHAP.  II.  §§  88,  89]     THERMAL   WORK   ON    ISOMERISM.  177 

Heat  of  combustion. 

(i)  alcohol,  330,000  gram- units. 

Empirical  formula  H3C  — CH2— OH 

C  H  O 

2    6  (2)  methylic  oxide  344,ooo  gram-units. 

H3C-0-CH3 

We  have  here  two  molecules  each  containing  a  pair  of  tetra- 
valent  carbon  atoms,  one  divalent  oxygen  atom,  and  six 
monovalent  hydrogen  atoms,  but  in  one  of  the  molecules 
each  carbon  atom  directly  interacts  with  three  hydrogen  and 
one  oxygen  atoms,  while  in  the  other  the  arrangement  of 
the  atomic  interactions  is  less  symmetrical. 

Other  examples  are  afforded  by  the  following  groups  of 
compounds : — 

Heat  of  combustion. 

(1)  allyl  alcohol 443,000  gram-units. 

CH2.CH.CH2OH 

(2)  propaldehyde 426,000    „        „ 

CH,.CH2.CHO 

(3)  acetone    424,000    „        „ 

CH3.CO.CH3 

f(i)  methyl  formate   252,000    „         „ 
H . COOCH3 
, . 

C  H  O.  (2)  acetic  acid  210,000    „        „ 

(  CH3.COOH 

/( i )  ethyl  acetate   554,ooo    „ 

IH.  CH3.CO.OCH2.CH3 

Empirical  formula  ] 

C4H,O2  (2)  butyric  acid     497,ooo    „ 

(  CH(CH3)2.COOH 

1(1)  i  :  4  hydroxybenzoic  acid, 
C0H4(OH)C02H     752,000     „ 

— -r---  --,(2)  !  :  3  „  „  754,000    „ 

1(3)  i  =2  „  „  759,ooo    „ 

89        The  data  are  not  sufficient  to  warrant  any  precise  state- 
ment as  to  the  relations  between  greater  or  smaller  quantities 
of  energy  and  molecular  structure.     It  is  possible  that  the 
case  of  benzene  and  dipropargyl  is  typical,  and  that  of  two 
M.  C.  12 


178  ATOMIC   AND   MOLECULAR   SYSTEMS.          [BOOK  I. 

isomeric  molecules  one  of  which  belongs  to  the  class  of 
ring-formed  and  the  other  to  that  of  open-chain  molecules, 
the  former  always  contains  relatively  less  energy  than  the 
latter.  It  is  also  possible  that  of  two  isomeric  carbon  com- 
pounds the  molecules  of  which  belong  to  the  open-chain 
class,  and  in  which  nl  <  2«4  +  ...  2,  that  containing  the  greater 
number  of  tetravalent  carbon  atoms  contains  the  smaller 
quantity  of  energy,  provided  that  the  distribution  of  the 
atomic  interactions  is  the  same,  or  nearly  the  same,  in  the 
two  molecules.  Or  again  it  may  be  that  when  the  actual 
valencies  of  the  atoms  in  two  or  more  isomeric  molecules 
are  the  same,  that  molecule  in  which  the  atomic  interactions 
are  distributed  so  as  to  produce  the  greatest  degree  of  sym- 
metry is  marked  by  the  smallest  amount  of  energy1.  But 
we  have  as  yet  no  accurate  knowledge  which  may  enable  us 
to  test  the  applicability  of  these  suggestions. 

Even  if  it  could  be  asserted  (as  seems  possible  in  a  few 
cases)  that  this  isomeride  contains  relatively  less  energy  than 
that,  and  is  therefore  more  stable,  the  question  would  arise, 
what  do  we  mean  by  stability  ?  For  although  of  two  mole- 
cules one  may  be  the  more  stable  as  stability  is  measured  by 
thermal  changes,  it  may  nevertheless  be  impossible  to  say 
that  this  molecule  is  possessed  of  greater  chemical  stability 
than  the  other.  But  a  discussion  of  the  meaning  and  appli- 
cation of  the  expression  chemical  stability,  requiring  as  it 
does  a  knowledge  of  the  facts  and  theories  of  chemical  affinity, 
will  find  a  fitter  place  in  that  part  of  this  book  which  deals 
with  chemical  kinetics2. 

Inasmuch  as  variations  in  the  physical  properties  of  ma- 
terial systems  accompany  variations  in  the  energies  of  these 
systems,  it  follows,  if  the  two  very  general  assumptions  made 
on  p.  175  concerning  the  connexion  between  the  energy  and 
the  structure  of  isomeric  molecules  are  granted,  that  physical 
phenomena,  other  than  thermal,  may  be  expected  to  exhibit 
variations  in  isomeric  molecules. 

1  This  view  is  put  forward  tentatively  by  Carnelley,  Phil.  Mag.  [5]  13.  180. 
The  data  given  on  p.  177  for  alcohol  and  methylic  oxide  are  not  in  keeping  with 
this  suggestion. 

2  See  Book  n. 


CHAP.  II.  §§89,90]       PHYSICAL   WORK   ON    ISOMERISM.          1/9 

An  attempt  will  be  made  in  a  future  chapter  to  summarise 
the  more  important  physical  phenomena  between  which  and 
molecular  structure  in  general  there  is  an  established  con- 
nexion (Chapter  IV.).  Here  I  would  only  remark  that  the 
researches  of  various  chemists  on  the  '  specific  volumes '  of 
liquid  compounds  seem  to  shew  that  the  influence  of  any 
atom  on  the  'specific  volume'  of  a  compound  molecule  is 
dependent,  not  only  on  the  nature  and  the  actual  valency 
of  that  atom,  but  also  on  the  nature  of  the  other  atom,  or 
atoms,  between  which  and  the  given  atom  there  is  direct 
interaction.  It  is  also  probable  that  while  the  influence 
exerted  by  a  polyvalent  atom  on  the  '  molecular  refraction ' 
of  isomeric  carbon-containing  molecules  is  to  a  large  extent 
dependent  on  the  actual  valency  of  that  atom,  nevertheless 
this  influence  is  also  sometimes  connected  with  the  nature  of 
the  other  atoms  between  which  and  the  given  atom  there  is 
direct  interaction  in  the  molecule  (j.  Chapter  IV.  Sect.  2). 
i  Much  is  to  be  expected  from  researches  into  the  phe- 
nomena which  occupy  the  border-land  between  chemistry 
and  physics.  If  the  knowledge  chemists  already  have  of  the 
structure  of  molecules,  meagre  though  that  knowledge  be,  can 
be  supplemented  by  definite  dynamical  conceptions,  obtain- 
able in  part  by  the  methods  of  thermal  chemistry,  then  we 
may  hope  that  chemistry  will  enter  on  a  new  stage  of  advance 
as  a  branch  of  the  science  of  matter  and  motion.  It  seems  to 
me  that  a  most  important  step  will  be  made  by  abandoning 
the  vague  conception  of  atomic  valency  which  finds  ex- 
pression in  such  phrases  as  'single  and  double  bonds,' '  satis- 
faction of  one,  two,  or  more  valencies/  and  the  like;  with  this 
will  go  all  those  quasi-dynamical  expressions,  the  offspring 
of  loose  and  slipshod  ways  of  thinking,  which  have  gathered 
round  that  strange  anomaly,  a  '  unit  of  affinity,'  employed  as 
a  variable  standard  for  measuring  nothing. 

If  it  is  decided  that  the  valency  of  an  atom  expresses 
the  maximum  number  of  other  atoms  between  which  and  the 
given  atom  there  is  direct  interaction  in  any  molecule,  and 
if  it  is  agreed  to  measure  this  valency  by  the  maximum 
number  of  monovalent  atoms  (i.e.  atoms  of  hydrogen,  fluorine, 

12—2 


180  ATOMIC  AND   MOLECULAR   SYSTEMS.          [BOOK  I. 

chlorine,  bromine,  or  iodine)  which  combine  with  the  specified 
atom  to  form  a  molecule,  then  we  are  put  in  possession 
of  a  definite  conception  which  may  be  applied  to  actually 
occurring  phenomena,  and  the  application  of  which  will 
gradually  lead  to  more  precise  knowledge  regarding  the 
distribution  of  the  atomic  interactions  in  various  molecules. 
But  at  the  same  time  that  we  are  classifying  molecules  in 
accordance  with  the  valencies  of  their  constituent  atoms  and 
the  distribution  of  the  interactions  of  these  atoms,  i.e.  in 
accordance  with  their  structure,  we  are  also  becoming  more 
impressed  with  the  inadequacy  of  this  classification  ;  we  see 
a  vast  field  opening  for  investigation,  we  see  that  measure- 
ments of  losses  or  gains  of  energy  are  required,  and  that 
determinations  of  many  physical  constants  are  called  for. 
We  begin,  I  think,  to  perceive  that  this  knowledge,  when 
gained,  will  supplement  and  not  supplant  that  which  is 
already  possessed  by  us,  and  that  it  will  do  this  by  leading  to 
an  exact  knowledge  of  the  way  in  which  the  variations  in 
the  energies  of  molecules  are  connected  with  changes  in  the 
configurations  and  motions  of  the  atoms  which  constitute 
these  molecules. 

91  Granting  that  the  definition  of  valency  given  by  Lessen 
furnishes  a  better  working  hypothesis  than  any  other,  we 
must  nevertheless  admit  that  several  compounds  present 
phenomena  which  seem  to  find  no  explanation  in  terms  of  the 
hypothesis  of  isomerism  which  arises  out  of  the  notion  of 
valency,  if  that  hypothesis  is  limited  as  was  done  in  par.  75. 
If  the  best  studied  examples  of  these  exceptional  compounds 
are  classified1  it  will,  I  think,  be  apparent ;  that  structural 
formulae  in  keeping  with  reactions  may  be  assigned  to  some 
of  the  isomeric  compounds  mentioned  provided  we  cease  to 
regard  the  conventional  method  of  expressing  valency  by  one 
or  more  straight  lines,  as  affording  any  quantitative  measure- 
ments, even  relative  measurements,  of  atomic  interactions ; 
that  some  cases  of  unexplained  isomerism2  are  probably 

1  See  especially  the  article  Isomerism  in  Watts's  Dictionary  [ist  Ed.],  Suppl. 
m.  (1881). 

2  That  optical  properties  are  not  always  dependent  on  the  structure  of  the 


CHAP.  II.  §§91,92]          GEOMETRICAL   ISOMERISM.  l8l 

illustrations  of  modifications  in  properties  being  correlated 
with  variations  in  mutual  actions  between  groups  of  molecules 
rather  than  between  the  atoms  constituting  each  molecule; 
and  that  the  remaining  cases  are  true  residual  phenomena, 
at  present  inexplicable  in  terms  of  the  generally  accepted 
hypothesis  but  not  therefore  of  necessity  destructive  of  this 
hypothesis. 

92  One  of  the  limitations  almost  universally  placed  on  the 
application  of  the  molecular  and  atomic  theory  to  explain 
the  facts  of  isomerism  consists  in  simplifying  the  phenomena 
to  be  explained  by  assuming  that  the  atoms  which  form  a 
molecule  are  arranged  in  one  plane. 

Chemists  have  always  recognised  that  a  complete  me- 
chanical conception  of  the  atomic  structure  of  a  molecule  was 
impossible  unless  the  conception  included  the  spatial  arrange- 
ment of  the  atoms  which  form  the  molecule.  Attempts  have 
been  made  from  time  to  time  to  formulate  such  a  conception, 
van't  Hoff1,  following  Le  Bel2,  in  1875  tried  to  gain  a  definite 
notion  of  the  spatial  arrangement  of  the  atoms  forming  the 
molecules  of  certain  carbon  compounds.  Considering  the 
molecule  CRRRR,  where  each  R  represents  a  different  mono- 
valent  atom  or  atomic  group,  van't  Hoff  supposed  the  carbon 
atom  to  be  placed  at  the  centre  of  a  regular  tetrahedron  and 
each  monovalent  radicle  to  be  placed  at  one  of  the  summits ; 
two  different  tetrahedra  would  thus  result,  bearing  to  each 
other  the  relation  of  an  object  to  its  reflected  image,  and 
incapable  of  being  superposed  in  whatever  position  they  may 
be  placed. 

The  more  immediate  object  of  this  conception  was  to 
connect  the  power  of  rotating  the  plane  of  polarisation  of  a 
ray  of  light  possessed  by  certain  compounds  of  carbon  with 
the  atomic  structure  of  the  molecules  of  these  compounds 
(for  more  details  s.  Chap.  iv.  par.  416).  Wislicenus  has 

molecule  is  shewn  by  the  ease  with  which  optically  active  amylic  alcohol  and 
valeric  acid  are  converted  into  the  inactive  alcohol,  and  acid,  without  change  of 
chemical  properties.  See  Armstrong  and  Groves,  Organic  Chemistry,  p.  449. 

1  La  Chitnie  dans  I '£ 'space. 

-  Bull.  Soc.  Chim.  22.  337 ;  23.  395. 


1  82  ATOMIC  AND   MOLECULAR   SYSTEMS.  [BOOK  1- 

recently  extended  the  notions  of  van't  Hoff  and  Le  Bel 
regarding  the  spatial  arrangement  of  atoms  ;  he  has  en- 
deavoured to  shew  that  the  greater  number,  if  not  all,  of  the 
well-established  facts  of  isomerism  which  lie  outside  of  the 
ordinary  hypothesis  find  an  explanation  in  terms  of  the  geo- 
metrical conception  of  the  molecule  suggested  by  van't  Hoff  1. 
93  Although  atomic  valencies  can  be  accurately  determined 
only  by  the  examination  of  a  certain  class  of  gaseous  mole- 
cules, yet  we  may  carry  over  the  general  conception  of 
limited  direct  atomic  interactions  from  gaseous  molecules  and 
apply  it  to  the  reacting  atomic  aggregates  of  solid  and  liquid 
compounds.  This  is  done  by  Wislicenus.  Most  of  the  phe- 
nomena to  be  explained  are  exhibited  by  compounds  of 
carbon  which  cannot  be  gasified  without  decomposition. 
Wislicenus  assumes  that  in  the  molecules  or  atomic  aggregates 
of  these  compounds  no  carbon  atom  can  directly  interact 
with  more  than  four  other  atoms. 

The  geometrical  conception  which  Wislicenus  forms  of  the 
molecule  of  a  carbon  compound  is  that  each  carbon  atom  is 
situated  at  the  centre  of  a  regular  tetrahedron,  and  that  each 
can  directly  interact  with  four  other  atoms  or  radicles  situated 
relatively  to  the  carbon  atom  as  the  four  summits  of  a  regular 
tetrahedron  are  situated  relatively  to  the  centre.  A  molecule 
containing  a  pair  of  tetravalent  ('singly  linked')  carbon  atoms 
of  the  general  form  C^g,  where  «  =  amonovalent  atom  or  radicle, 
is  represented  by  two  tetrahedra  with  one  pair  of  common 
summits;  a  molecule  containing  a  pair  of  trivalent  ('doubly 
linked  ')  carbon  atoms  —  C^4  —  is  represented  by  two  tetrahedra 
with  two  pairs  of  common  summits  ;  and  a  molecule  con- 
taining a  pair  of  divalent  ('  trebly  linked  ')  carbon  atoms 
—  C^2  —  is  represented  by  two  tetrahedra  with  three  pairs  of 
common  summits.  Figures  I,  2,  and  3  represent  these  geo- 
metrical conceptions. 

In  a  molecule  of  the  composition  C^&j,  where  a^  repre- 


1  ttber  die  raumliclie  Anordnung  der  Atome  In  organischen  Molekulen 
und  ilire  Bestimmung  in  geometrischen-isomeren  ungesattigten  Verbindungen. 
Konigl.  Siichsischen  Gesellschaft  der  Wissenschaften  (inath-physische  Classe)  Bd. 
l-l.  i. 


CHAP.  1 1.  §93] 


GEOMETRICAL   ISOMERISM. 


sents  two  identical  monovalent  atoms  or  radicles,  and  #2  repre- 
sents two  monovalent  atoms  different  from  a,  chemical  iso- 


merism  may  arise  because  of  different  arrangements  of  the 
atoms  ;  thus  we  may  have 

b  a  a  a 


(0 


C  — C 


c  — c 


but  the  second  of  these  isomerides  may  exist  in  two  forms 
which  are  geometrically  different  although  structurally  the 
same,  and  either  of  these  geometrical  isomerides  will  bear  to 
the  other  the  relation  of  an  object  to  its  image.  The  three 
forms  of  C^/2  are  represented  in  figs.  4,  5,  and  6. 

Fig.  4.  Fig.  5.  Fig.  6. 

1* 


Similarly  a  molecule  of  the  composition  C2 
chemical  isomerism  ; 

b  a  a 


C  — C 


and 


\ 


C  — C     : 

'  \ 


may  shew 


184 


ATOMIC  AND   MOLECULAR   SYSTEMS.          [BOOK  I. 


but  the  second  isomeride  may  also  exhibit  geometrical  iso- 
merism.  A  molecule  of  the  form  C^abcd  may  exist  in  three 
isomeric  modifications,  each  of  which  may  exist  in  two  geo- 
metrically different  forms.  Figs.  7  to  15  represent  these 
isomerides. 

Fig.  7.  Fig.  8.  Fig.  9. 


Fig.  10. 


Fig.  13- 


Fig.  14. 


Fig.  15- 


The  terms  axially  symmetric  and  plane-symmetric  are  used 
to  distinguish  geometrical  isomerides  of  the  composition 
Cotfj^.  A  molecule  the  configuration  of  which  is  shewn  in  fig. 
1 6  is  called  by  Wislicenus  axially  symmetric,  because  the 
atoms  a  and  b  are  represented  as  arranged  symmetrically 
about  an  axis  passing  between  the  two  pairs  of  common 


CHAP.  II.  §§93,  94]         GEOMETRICAL   ISOMERISM.  185 

summits ;   the  geometrically  isomeric  molecule  shewn  in  fig. 
17  is  called  plane-symmetric  because  the  atoms  a  and  b  are 

Fig.  16.  Fig.  17. 

it 


represented  as  arranged  symmetrically  about  a  plane  passing 
through  the  two  pairs  of  common  summits. 

94  Wislicenus  developes  these  conceptions  chiefly  for  mole- 
cules containing  two  carbon  atoms.  When  the  molecule 
contains  a  pair  of  divalent  ('trebly  linked')  carbon  atoms 
geometrical  isomerism  cannot  occur;  when  the  molecule 
contains  a  pair  of  trivalent  ('doubly  linked')  carbon  atoms  geo- 
metrical isomerism  may  occur  in  the  manner  illustrated  in 
the  preceding  paragraph ;  when  the  molecule  contains  a  pair 
of  tetravalent  ('  singly  linked  ')  carbon  atoms  geometrical  iso- 
merism may  occur  by  the  rotation  of  one  part  of  the  molecule 
relatively  to  the  other.  This  last  kind  of  isomerism  is  illus- 
trated by  figs.  1 8  and  19.  The  cause  of  this  rotation  of  one  part 


Fig.  1 8. 


Fig.  19. 


of  a  molecule  containing  a  pair  of  tetravalent  carbon  atoms 
is  supposed  by  Wislicenus  to  be  the  affinities1  of  the  atoms 

1  The  term  affinity  is  here  used  to  express  the  unknown  property  of  atoms  by 
reason  of  which  they  chemically  interact. 


186  ATOMIC   AND   MOLECULAR   SYSTEMS.          [BOOK  1. 

other  than  carbon  ;  the  configuration  of  the  molecule  tends 
to  become  that  in  which  the  atoms  with  the  largest  affinities 
are  situated  nearest  to  each  other. 

But  besides  the  affinities  of  the  atoms,  heat  will  probably 
produce  rotation  of  the  parts  of  a  molecule  containing  only 
tetravalent  carbon  atoms.  The  most  stable  atomic  configura- 
tion will  be  that  caused  by  the  mutual  atomic  affinities  ;  but 
besides  this,  some  configurations  will  probably  exist,  and  will 
likely  increase  in  number  as  temperature  rises,  which  con- 
figurations are  caused  by  the  action  of  heat ;  at  high  tem- 
peratures therefore  a  given  compound  will  probably  be 
composed  for  the  greater  part  of  molecules  the  atomic  con- 
figuration of  which  is  determined  by  the  atomic  affinities,  but 
other  and  less  stable  configurations  will  also  be  present. 

If  a  molecule  containing  a  pair  of  divalent  ('trebly  linked') 
carbon  atoms  combines  with  two  monovalent  atoms  of  the 
same  kind,  or  of  different  kinds,  only  one  geometrical  isomer- 
ide  can  be  produced.  If  a  molecule  containing  a  pair  of 
trivalent  ('doubly  linked  ')  carbon  atoms,  one  or  both  of  which 
atoms  is  in  direct  union  with  two  monovalent  atoms  of  the 
same  kind,  combines  with  two  new  atoms  two  geometrical 
isomerides  may  be  produced ;  in  some  cases  the  isomerides 
so  produced  will  contain  an  asymmetric  carbon  atom,  i.e. 
an  atom  in  direct  union  with  four  different  atoms  or  groups. 
Thus  if  the  original  molecule  is  of  the  form 

a  a 

\  / 

C  — C 

/  \ 
a  b 

and  the  new  molecule  is  of  the  form 

a  a 

\          / 
a  —  C  —  C  —  b, 
/  \ 

c  c 

the  italicised  C  represents  an  asymmetric  carbonation.  In 
such  a  case  the  compound  thus  produced  should  exhibit  optical 

1  See  Chap.  iv.  par.  146. 


CHAT.  II.  §§94- 95]        GEOMETRICAL   ISOMEKISM. 


18; 


activity,  if  the  hypothesis  of  van  t  Hoff  is  adopted  (s.  Chap.  IV.) 
But  such  reactions  are  sometimes  known  to  produce  com- 
pounds which  do  not  shew  optical  activity.  Wislicenus  sup- 
poses that  in  these  cases  the  two  geometrical  isomerides  are 
produced  in  equal  quantities,  and  that  as  one  is  dextrorota- 
tory and  the  other  laevorotatory  the  compound  as  a  whole  is 
optically  inactive.  The  foregoing  statements  are  rendered 
clearer  by  examining  figs.  20  to  27. 


Fig.  20. 


Fig.  21. 


Fig.  23- 


Fig.  24.  Fig.  25.  Fig.  26.  Fig.  27. 


95  Wislicenus  developes  these  conceptions  and  applies  them 
to  many  cases  of  isomerism  which  do  not  find  an  explanation 
in  terms  of  the  hypothesis  of  valency  when  it  is  limited  by 
the  condition  that  the  atoms  which  form  a  molecule  must  be 
represented  as  arranged  in  a  single  plane. 

Thus  to  take  the  cases  of  fumaric  and  maleic  acids, 
C2H2(CO2H)2.  Fumaric  acid  is  probably  the  axially  sym- 
metric, and  maleic  acid  the  plane-symmetric,  isomeride ;  figs. 
28  and  29  represent  these  compounds.  When  malic  acid 
C2H3(OH)(CO8H)a  is  heated  to  about  150°  water  is  separated 
and  fumaric  acid  is  formed;  this  change  is  represented  in 


1 88  ATOMIC   AND   MOLECULAR   SYSTEMS.          [BOOK  I. 

figs.   30   and    31.     But   at    170° — 180°   malic  acid    is   partly 
changed    to   maleic  anhydride ;   if  we  suppose  that   rise  of 

Fig.  29. 


COOJl 


Fig.  30. 


Fig.  31- 


temperature  causes  rotation  of  the  parts  of  the  molecule  of 
malic  acid  with  the  production  of  a  geometrical  form  less 
stable  than  the  original  form,  and  that  water  is  then  separated 
from  this  less  stable  form,  we  can  explain  the  production  of 
maleic  anhydride  along  with  fumaric  acid  by  heating  malic 
acid.  Figs.  32  and  33  (taken  with  fig.  30)  represent  this  process. 
Fig.  32.  Fig.  33. 


Maleic  acid  is  changed  almost  wholly  to  fumaric  acid  by 
interacting   with   hydrochloric   or   hydrobromic   acid.      Wis- 


CHAP.  II.  §95]  GEOMETRICAL   ISOMERISM. 


I89 


licenus  supposes  that  an  additive  compound  is  produced, 
that  rotation  of  the  parts  of  this  molecule  then  occurs  caused 
by  the  affinities  of  the  atoms  H  and  Br  and  the  group 
COOH,  and  that  HBr  is  then  split  off;  the  mechanism  of 
the  change  as  thus  imagined  is  shewn  in  figs.  34  to  37. 

Fig-  34-  Fig.  35. 


COOH 


Fig-  36- 


Fumaric  acid  combines  with  bromine  forming  dibromo- 
succinic  acid,  which  when  boiled  with  water  yields  hydro- 
bromic  and  bromomaleic  acids.  Maleic  acid  combines  with 
bromine  forming  isodibromosuccinic  acid,  and  this  when 
boiled  with  water  yields  hydrobromic  and  bromofumaric 
acids.  These  changes  are  easily  explained  in  terms  of  Wisli- 
cenus'  conception,  by  supposing  that  in  each  case  an  additive 
compound  is  formed,  that  the  atomic  affinities  then  cause 
rotation  of  the  parts  of  the  molecules,  and  that  hydrobromic 
acid  is  then  split  off.  Figs.  38  to  45  represent  the  changes. 

Other  reactions  of  fumaric  and  maleic  acid  are  considered 
and  explained  by  Wislicenus.  The  only  reaction  of  these 
acids  which  is  inexplicable  in  terms  of  the  geometrical  hypo- 
thesis of  isomerism  is  that  of  bromine  with  acetylene  di- 


1 9o 


ATOMIC   AND   MOLECULAR   SYSTEMS.          [BOOK  I. 


carboxylic  acid,  C2(CO2H)2,  whereby  dibromofumaric  acid  is 
said  to  be  produced.     The  geometrical   hypothesis  requires 


Fig.  38- 


Fig.  40. 


the  production  of  dibromomaleic  acid.  But  Wislicenus'  ex- 
periments have  proved  that  hydrobromic  acid  is  always  pro- 
duced in  this  reaction,  and  that  if  care  is  taken  to  limit  the 
yield  of  this  acid  as  much  as  possible,  some  dibromomaleic 
acid  is  produced.  The  production  of  dibromofumaric  acid 
is  easily  explained  by  the  interaction  of  the  hydrobromic 
and  bromomaleic  acids  produced  in  the  principle  reaction. 


CHAP.  II.  §§95, 96]  RECAPITULATION.  191 

There  can  be  no  doubt  as  to  the  ingenuity  of  the  ex- 
tension of  van't  HofFs  geometrical  conception  made  by  Wis- 
licenus.  One  point  which  appears  to  me  to  be  gained  by 
this  hypothesis  is  the  possibility  of  keeping  separate  the  two 
conceptions  of  atomic  valency  and  atomic  affinity,  and  of 
using  both  in  explaining  the  configurations  and  chemical 
properties  of  molecules. 
E)6  We  have  thus  found  that  to  trace  the  connexions  between 
the  compositions  and  the  properties  of  changing  material 
systems  has  always  been  regarded  as  the  fundamental  problem 
of  chemistry.  Attention  has  sometimes  been  almost  confined 
to  the  composition  of  substances  forming  such  systems,  at  other 
times  the  properties  of  the  systems  and  their  components 
have  been  regarded  as  chiefly  important.  We  found  that  as 
chemistry  advanced  it  became  necessary  to  know  more  than 
the  mere  elementary  composition  of  bodies ;  having  gained 
the  atom  and  the  molecule,  chemists  were  soon  convinced 
'that  the  arrangement  of  the  same  atoms  might  vary,  and  that 
properties  might  therefore  be  correlated  not  only  with  atomic 
composition  but  also  with  atomic  configuration.  We  traced 
this  conception  through  the  dualism  of  Berzelius  and  the 
unitary  system  of  Dumas,  Laurent,  Gerhardt  and  others, 
through  the  hypothesis  of  compound  radicles  and  that  of 
types,  to  the  time  when  Frankland  and  Kekul6  gave  it 
greater  precision  by  arranging  the  elementary  atoms  in 
groups  according  to  the  maximum  number  of  other  atoms 
with  which  each  was  found  to  combine. 

But  we  saw  that  the  expression  equivalency,  or  valency, 
of  atoms  gradually  came  to  be  used  in  a  loose  and  inexact 
manner.  We  found  that  the  comparison  of  monovalent  with 
divalent,  &c.  atoms,  when  unchecked  by  accurate  dynamical 
knowledge,  led  to  the  belief  that  the  terms  in  question  ex- 
pressed in  some  vague  way  quantitative  measurements  of 
interatomic  forces,  and  to  the  conclusion  that,  inasmuch  as 
one  divalent  atom  could  directly  bind  to  itself  two  other 
atoms,  while  one  monovalent  atom  could  directly  interact 
with  only  a  single  other  atom,  in  a  molecule,  therefore  the 
divalent  atom  was  capable  of  exerting  twice  as  much  force 


192  ATOMIC   AND   MOLECULAR   SYSTEMS.          [BOOK  I. 

as  the  monovalent  atom.  The  latter  part  of  the  foregoing 
sentence  may  I  think  be  taken  as  fairly  representative  of  the 
loose  and  slipshod  way  in  which  dynamical  language  has  too 
often  been  used  in  chemistry. 

We  found  that  attempts  were  made  to  build  a  general 
conception  of  atomic  valency  on  a  shifting  quasi-dynamical 
foundation  ;  but  the  account  given  in  this  section  of  Lossen's 
criticisms  of  the  expressions  'a  bond,'  'a  valency,'  'a  unity  of 
affinity,'  &c.  has  I  think  been  sufficient  to  shew  how  inexact, 
while  apparently  precise,  and  how  narrow,  while  apparently 
far-reaching,  the  conception  in  question  really  is. 

The  objections  raised  against  the  atomic  theory  in  recent 
years  by  some  chemists,  who  nevertheless  made  free  use  of 
the  essentially  atomic  conceptions  of  modern  chemistry,  led, 
it  seems  to  me,  to  a  looseness  of  thinking  about  atoms,  mole- 
cules, and  equivalents,  which  has  done  no  little  harm.  Parts 
by  weight  were  spoken  of  as  if  the  expression  were  synony- 
mous with  atom;  equivalents  were  regarded  as  acting  and 
reacting  with  one  another ;  there  appeared  to  be  a  possibility 
of  chemistry  retracing  her  steps  to  the  time  when  no  precise 
meaning  was  attached  to  any  of  the  terms  atom,  molecule, 
combining  weight,  equivalent,  but  each  was  used  as  nearly 
synonymous  with  the  others.  From  the  possibility  of  such 
retrogression  we  have  been  saved  by  the  general  advance  of 
physical  science.  As  the  molecular  theory  of  matter  became 
more  precise  and  its  applications  more  far-reaching,  it  was 
impossible  for  chemists  to  employ  conceptions  essentially 
molecular  and  atomic  and  at  the  same  time  to  express 
chemical  changes  in  a  notation  based  on  the  notions  of  a 
pre-molecular  era.  It  became  necessary  to  choose  definitely 
between  the  atom  and  the  equivalent,  and  the  great  body  of 
chemists  has  certainly  chosen  the  former. 

But  as  soon  as  attempts  to  found  a  conception  of  chemical 
actions  on  the  basis  of  equivalents  were  abandoned,  it  was 
seen  that  the  conception  of  equivalency  might  be  retained 
and  applied  to  the  elementary  atoms.  To  keep  distinct  the 
conceptions  implied  in  the  terms  equivalent  and  atom,  and  at 
the  same  time  to  arrange  the  atoms  in  equivalent  groups,  is 


CHAP.  II  §96]  RECAPITULATION.  193 

one  of  the  problems  of  modern  chemistry.  On  this  distinction 
and  on  this  resemblance  is  based  the  molecular  explanation 
of  isomerism.  We  have  found  that  the  study  of  isomerism 
has  done  much  to  render  precise  the  conception  of  the  mole- 
cule as  a  structure  with  properties  dependent  on  the  nature, 
the  number,  and  the  arrangement,  of  the  constituent  atoms. 

We  endeavoured  to  subdivide  the  conception  expressed  in 
the  words  '  arrangement  of  atoms  in  a  molecule '  into  parts, 
and  to  demonstrate  by  illustrations  the  existence  of  a  con- 
nexion between  each  of  these  parts  and  the  properties  of  the 
molecule.  These  illustrations  led  to  clearer  notions  concern- 
ing the  valencies  of  atoms,  and  the  meaning  of  structural 
formulae:  these  formulae  we  regarded  as  expressing  the  actual 
valencies  of  the  atoms  in  the  molecule,  i.e.  the  number  of  atoms 
directly  acting  on  and  acted  on  by  each  atom,  and  as  ex- 
pressing also  the  distribution  of  the  atomic  interactions,  i.e. 
the  nature  of  the  atoms  in  direct  mutual  connexion  ;  but  we 
tried  not  to  attach  any  quantitative  meaning  to  the  symbols 
used  for  expressing  atomic  valencies  and  the  distributions  of 
atomic  interactions.  We  also  glanced  at  the  geometrical  con- 
ception by  which  van't  Hoff  and  Wislicenus  have  sought  to 
picture  the  connexion  between  the  properties  of  isomeric 
molecules  and  the  configurations  of  the  atoms  which  form 
these  molecules. 

The  hypothesis  of  valency  as  thus  used  leads  to  dynamical 
conceptions  but  regards  these  as  outside  its  sphere  :  it  points 
the  way  along  which  progress  will  be  made.  Attempts  must 
be  made  to  apply  thermal,  optical,  and  other  physical,  methods 
of  research  to  the  investigation  of  chemical  problems ;  thus 
we  may  hope  to  gain  clear  and  precise  knowledge  regarding 
the  connexion  between  the  structure  and  the  stability  of  mole- 
cules, in  so  far  as  the  latter  is  measured  by  variations  in  the 
quantities  of  energy  associated  with  different  molecules. 

APPENDIX  TO  SECTION  IV. 

To   have   given   a   detailed   account   of   Lossen's   criticisms    of   the 

generally  accepted  views  regarding  'valencies'  or  'units  of  affinity'  in 

the  text  of  the  section  on  isomerism,  would   have  involved  too  great 

an  interruption  of  the  main  argument  of  that  section.     But  as  Lossen's 

M.C.  13 


194  ATOMIC   AND   MOLECULAR   SYSTEMS.          [BOOK  I. 

criticisms  seem  to  me  of  great  importance  I  propose  to  give  some  account 
of  them  here. 

The  many  and  varied  hypotheses  concerning  valency  set  forth  by 
chemists  of  acknowledged  authority  may  be  divided,  says  Lessen,  into 
three  groups  :— 

I.  Those  hypotheses  which  regard  'an  affinity'  as  a  definite  quantity 
of  matter,  or  as  an  action  of  some  kind  proceeding  from  a  definite 
quantity  of  matter. 

II.  Those  which  regard  'an  affinity'  as  a  part  of  an  atom,  or  at 
least  as  something  connected  with  a  part  of  an  atom. 

III.  Those  which  regard  the   'affinities'   of  an   atom   as   definite 
forms  of  motion  of  the  atom. 

I.  Erlenmeyer1  has  developed  the  conception  of  ' Affinivalencies? 
He  states,  as  a  rule  without  exceptions,  that  "in  all  chemical  combi- 
nations a  constant  quantity  of  one  element  always  attracts  a  constant 
quantity  of  another."  These  constant  quantities  are  the  '  affinivalencies  ' 
of  the  elements:  one  affinivalency  of  element  a  always  binds  to  itself 
one  affinivalency  of  element  b.  The  affinivalency  of  carbon  =  3,  of 
oxygen  =  8.  Now  in  CO2  we  have  3  parts  by  weight  of  carbon  com- 
bined with  8  of  oxygen,  but  in  CO  the  same  amount  of  carbon  with 
only  4  parts  by  weight  of  oxygen ;  Erlenmeyer's  general  law  does  not 
therefore  always  hold  good.  If  it  be  said  that  a  constant  quantity  of 
one  element  attracts  (not  combines  with)  a  constant  quantity  of  another, 
then,  as  in  CO2  6  parts  by  weight  of  carbon  attract  16  of  oxygen,  we 
must  suppose  that  in  CO  16  parts  by  weight  of  oxygen  are  attracted 
by  6  of  carbon,  and  that  the  remaining  6  of  carbon  have  no  attractive 
action  on  the  oxygen. 

Atoms  and  relative  quantities  of  matter  are  compared  by  Erlenmeyer ; 
but  relative  quantities  do  not  attract  each  other.  In  the  molecule  CO 
there  is  one  atom  of  carbon  and  one  atom  of  oxygen,  and  these  atoms 
attract  one  another;  half  an  atom  cannot  attract  because  it  has  no 
existence.  The  hypothesis  that  an  atom  is  non-homogeneous,  although 
indivisible,  might  be  made,  but  is  not  made,  by  Erlenmeyer.  If  an 
equivalent  is  regarded  as  a  constant  quantity,  this  quantity  attracts 
sometimes  one,  sometimes  two  (or  more)  equivalents  of  other  elements. 
The  molecule  CH4  is  composed  of  one  atom  of  carbon  and  four  atoms 
of  hydrogen,  we  may  say  that  3  parts  by  weight  of  carbon  here  attract 
i  part  by  weight  of  hydrogen ;  so  in  CC14  it  may  be  said  that  3  parts 
of  carbon  attract  35-5  parts  of  chlorine.  But  in  CH3C1  12  parts  of 
carbon  attract  3  parts  of  hydrogen  and  35-5  parts  of  chlorine ;  in  place 
of  12  parts  of  carbon  we  may,  if  we  choose,  say  9  +  3  parts,  just  as  we 
might  say  that  7  +  5  =  12,  or  Vi44=i2;  but  we  cannot  say  that  9  parts 

1  For  references  to  the  work  of  the  various  chemists  mentioned,  see  Lessen, 
Annalen,  204.  265  et  seq. 


CHAP,  ii.]    LOSSEN'S  CRITICISM  OF  '  BOND' HYPOTHESIS.    195 

of  carbon  attract  3  parts  of  hydrogen  and  the  remaining  3  parts  of 
carbon  attract  the  35-5  parts  of  chlorine.  If  we  suppose  the  carbon 
atom  to  be  perfectly  homogeneous,  then  the  whole  atom  interacts  with 
the  chlorine  atom  and  with  each  of  the  hydrogen  atoms ;  if  we  suppose 
that  the  atom  of  carbon  is  possessed  of  a  structure,  it  remains  to 
explain  in  what  respect  one  part  of  the  atom  differs  from  the  other 
parts :  but  a  part  of  an  atom  is  not  the  same  thing  as  a  fraction  of  the 
relative  weight  of  an  atom. 

Hofmann  speaks  of  'an  affinity'  as  a  force  proceeding  from  a  con- 
stant mass  of  an  element,  which  mass  he  regards  as  the  equivalent  and 
defines  as  'the  minimum  atom-binding  quantity'  of  the  element.  He 
nevertheless  uses  an  equivalent  as  a  varying  quantity.  By  an  arbitrary 
choice  of  certain  values  for  the  equivalents  of  the  elements  it  is  possible 
that  the  number  obtained  by  dividing  the  atomic  weight  by  the  equiva- 
lent weight  of  any  element  should  be  the  same  as  the  number  expressing 
the  maximum  number  of  hydrogen  atoms  which  can  be  bound  by  one 
atom  of  the  given  element. 

L.  Meyer  also  speaks  of  the  action  of  quantities  by  weight  of  one 
element  on  atoms  of  another  element.  In  one  place  he  defines  equiva- 
lent quantities  of  elements  as  those  quantities  which  are  able  to  bind 
to  themselves,  directly  and  without  the  intervention  of  a  third  substance, 
equal  quantities  of  other  substances.  We  should  expect  16  parts  by 
weight  of  oxygen  to  be  equivalent  to  12  parts  by  weight  of  carbon,  and 
to  14  parts  by  weight  of  nitrogen,  because  16  parts  of  oxygen  directly 
bind  16  of  oxygen  in  O2,  14  of  nitrogen  in  NO,  and  12  of  carbon  in 
CO ;  but  Meyer  supposes  two  free  affinities  in  the  last  named  molecule, 
i.e.  he  supposes  that  *£•  parts  of  carbon  bind  16  parts  of  oxygen,  although 
the  molecule  CO  contains  one  indivisible  atom  of  carbon  and  one  in- 
divisible atom  of  oxygen. 

Those  hypotheses  in  which  'affinities'  are  regarded  as  constant 
weights  of  matter,  or  as  actions  proceeding  from  constant  weights,  arise, 
according  to  Lessen,  from  not  sufficiently  marking  the  distinction  be- 
tween the  equivalent  and  the  atom.  Equivalent,  or  combining,  weights 
are  relative  weights  of  divisible  masses ;  atomic  weights  are  relative 
weights  of  indivisible  masses.  If  the  atomic  hypothesis  is  adopted  we 
must  regard  atomic  weights  as  relative  weights  of  mutually  reacting 
bodies  ;  but  equivalent  weights,  in  so  far  as  they  differ  from  atomic 
weights,  are  relative  weights  of  imagined  sums,  or  fractions,  of  these 
bodies.  Bodies  whose  relative  weights  are  equal  to  these  equivalent 
weights  do  not  mutually  react  in  molecules.  To  find  equivalents,  parts 
by  weight  should  be  compared  with  parts  by  weight,  or  atoms  with 
atoms. 

II.  Besides  the  hypothesis  of  'affinivalencies'  already  referred  to, 
Erlenmeyer  also  speaks  of  mutual  actions  between  atoms  as  occurring 
at  certain  points  of  these  atoms.  This  may  mean  either  that  contact 

13—2 


196  ATOMIC  AND   MOLECULAR   SYSTEMS.          [BOOK  I. 

(not  of  course  absolute  contact)  between  the  reacting  atoms  is  made 
at  these  points,  or  that  mutual  atomic  action  occurs  only  when  these 
attracting  points  coincide.  The  attracting  points  must  be  considered 
as  qualitatively  different  from  the  rest  of  the  atoms.  The  form  of  poly- 
valent atoms  must  be  such  that  several  points  of  one  can  touch  the 
same  number  of  points  of  another:  the  positions  of  the  points  must  be 
such  that  when  some  of  these  points  are  in  contact  it  is  not  necessary 
that  all  should  be  in  contact.  To  fulfil  these  conditions  without  sup- 
posing the  form  of  the  atoms,  or  at  any  rate  the  positions  of  the  points, 
changeable,  is  exceedingly  difficult.  This  hypothesis  of  Erlenmeyer 
tends  to  foster  the  notion  of  an  attractive  force  proceeding  from  different 
parts  of  elementary  atoms  ;  Kekule"'s  graphic  formulae  do  not,  probably, 
imply  this  conception,  but  these  formulas  may  be,  and  have  been,  used 
as  if  this  conception  were  true. 

A  qualitative  difference  between  parts  of  an  atom  can  only  mean 
that  some  parts  are  chemically  active  while  others  are  chemically  inactive. 
If  the  inactive  parts  are  composed  of  imponderable  matter  then  each 
«-valent  atom  must  be  made  up  of  n  atoms;  we  thus  arrive  at  atomic 
weights  different  from  those  on  which  the  science  of  chemistry  at  present 
rests.  If  the  inactive  parts  consist  of  ponderable  matter,  then  in  the 
case  of  action  between  different  atoms  we  have  action  through  the  ether, 
but  in  the  case  of  action  between  parts  of  the  same  atom  we  have  action 
through  ponderable  chemically  inactive  matter.  In  either  case  it  appears 
that  the  notion  of  atom  must  be  very  different  from  that  at  present 
adopted,  and,  it  would  seem,  necessarily  adopted  if  facts  are  to  be 
explained. 

But  it  may  be  supposed  that  the  active  parts  of  the  atom  are  in 
a  different  electrical  condition  from  the  inactive  parts.  If  electricity 
be  a  form  of  motion,  then  some  parts  of  an  indivisible  atom  must  be 
supposed  in  motion  while  others  are  not ;  if  electricity  be  a  fluid,  then 
we  have  a  material  difference,  arising  from  the  partial  fixation  of  this 
fluid,  between  the  active  and  inactive  parts  of  the  atom.  Both  of  these 
hypotheses  are  opposed  to  the  fundamental  conception  of  atom1. 

Michaelis  has  supposed  that  the  attractive  force  of  an  atom  is  exerted 
in  certain  fixed  directions  only.  On  this  hypothesis  a  straight  line 
joining  two  atoms  which  are  directly  bound  together  may  be  regarded 
as  expressing  the  direction  of  the  mutually  exerted  force;  an  «-valent 
atom  has  n  such  directions.  If  this  atom  is  directly  bound  to  fewer 
than  n  atoms,  say  to  n  -  x  atoms,  then  the  mutual  action  is  exerted 
in  n  —  x  directions.  Lessen  expresses  his  general  agreement  with  this 
interpretation  of  the  hypothesis  of  Michaelis.  But  if  that  chemist  sup- 

1  This  criticism  is  rather  weak :  we  know  too  little  as  to  what  electricity  is  to 
hazard  such  criticism  as  this ;  besides,  Helmholtz  has  shewn  that  there  is  probably 
a  close  and  definite  connexion  between  the  valency  of  an  atom  and  the  electrical 
charges  on  that  atom ;  see  Book  n. 


CHAP.  IL]  LOSSEN'S  CRITICISM  OF  *  BOND'  HYPOTHESIS.     197 

poses  that  to  every  atom,  regarded  as  a  point,  there  are  always  attached 
a  fixed  number  of  such  'lines  of  force,'  then  it  is  asked  'on  what  does 
the  atom  act  when  it  is  bound  to  less  than  its  maximum  number  of 
other  atoms?' 

The  objection  urged  to  van't  Hoff's  form  of  the  hypothesis  now  being 
discussed,  is,  that  by  this  chemist  the  'affinities'  of  an  atom  are  imagined 
as  arranged  in  a  definite  form  in  space ;  but  as  we  cannot  define  an 
'affinity,'  much  less  can  we  assign  geometrical  figures  to  the  arrange- 
ment of  these  'affinities'1. 

III.  L.  Meyer  supposes  that  there  is  one  position  at  which  a  mono- 
valent  atom  during  its  vibration  can  combine  with  another  atom  to 
form  a  stable  compound,  that  there  are  two  positions  at  which  a  divalent 
atom  can  combine  with  another  atom,  and  so  on.  In  the  molecule  NH3 
we  have  one  trivalent  and  three  monovalent  atoms;  the  nitrogen  atom 
swings  through  three  positions  at  each  of  which  it  can  take  up  one 
hydrogen  atom.  In  the  molecule  OH2  the  divalent  oxygen  atom  swings 
through  two  such  positions.  In  the  molecule  NO  it  appears  as  if  the 
three  positions  of  possible  combination  passed  through  by  the  triad 
nitrogen  atom  must  also  be  touched  by  the  path  of  the  diad  oxygen 
atom,  but  if  so  the  oxygen  atom  may,  in  some  circumstances,  be 
trivalent. 

The  results  of  O.  E.  Meyer's  physical  and  dynamical  investigation  of 
the  forms  of  molecules  are  not  in  harmony  with  this  view  of  L.  Meyer. 
The  form  of  a  molecule  would  appear  to  be  dependent  more  on  the 
number  of  the  constituent  atoms  than  on  the  valencies  of  these  atoms ; 
but  on  L.  Meyer's  hypothesis  the  nature  of  the  path  of  the  atoms  swinging 
in  the  molecule  must  condition  the  form  of  the  molecule,  and  the  nature 
of  this  path  is  itself  conditioned  by  the  valencies  of  the  atoms. 

Kekule'  has  advanced  hypotheses  as  to  the  motion  of  atoms  within 
molecules,  but  these  hypotheses  are  not  sufficiently  definite  to  admit 
of  detailed  criticism.  Lessen  however  objects  to  applying  to  the  motion 
of  atoms  within  molecules  the  conceptions  which  arise  from  a  study  of 
the  motion  of  molecules  in  a  confining  vessel.  If  the  atoms  composing 
a  mass  of  hydrogen  molecules  undergo  mutual  collisions,  why,  when 
they  have  separated  a  certain  distance  from  one  another,  is  the  direction 
of  their  motion  changed  until  a  second  collision  occurs?  There  is  no 
confining  molecular  wall  answering  to  the  sides  of  a  containing  vessel. 
If  it  be  supposed  that  the  atoms  in  molecule  a  enter  into  collision  with 
the  atoms  in  molecule  b  or  c,  then  this  is  equivalent  to  asserting  that 
a  mass  of  hydrogen  is  composed  not  of  diatomic,  but  of  monatomic 
molecules2. 

1  Van't  Hoffs  hypothesis  as  recently  developed  by  Wislicenus  is  discussed  in 
pars.  92  to  95. 

2  Here  again,  I  think  Lessen  carries  his  criticism  too  far.     The  methods  of 
molecular  enquiry  are  necessarily  statistical;    a  mass  of  hydrogen  may  contain 


198  ATOMIC   AND   MOLECULAR   SYSTEMS.          [BOOK  I. 

Among  the  various  developments  of  the  bond-hypothesis  of  valency 
not  mentioned  in  the  text,  is  that  which  concerns  itself  with  the  question 
whether  all  the  bonds  of  a  polyvalent  atom  are  of  equal  value,  or 
whether  one  maybe  'stronger'  than  another.  If  the  criticism  applied 
to  the  subject  of  bonds  generally  is  just,  it  follows,  I  think,  that  the 
question  alluded  to  is  meaningless;  but  as  it  has  been  hotly  disputed 
about  it  may  be  well  briefly  to  consider  it  here. 

It  is  assumed  in  the  bond-hypothesis  that  the  so-called  affinities  of 
atoms  attract  or  satisfy  one  another,  and  hence  those  affinities  of  one 
atom  which  are  not  satisfied  by  affinities  of  another  must  be  satisfied  by 
other  affinities  of  the  atom  itself.  No  molecule,  it  is  sometimes  said, 
can  contain  an  odd  number  of  atoms  of  uneven  valency.  This  outcome1 
of  Gerhardt's  'law  of  even  numbers'  (see  ante,  chap.  I.  p.  84)  is  how- 
ever contradicted  by  the  existence  of  the  molecules  I,  NO,  NO2,  C1O2, 
WC15,  VC14  or  VOC13,  and  cannot  therefore  be  accepted  as  a  statement 
of  facts,  unless  indeed  the  valency  of  an  atom  is  a  number  susceptible 
of  arbitrary  variation.  That  the  maximum  valency  of  each  atom  is 
fixed  is  generally  admitted.  One  school  however  holds  that  (e.g.)  a 
tetrad  atom  is  always  tetrad ;  another  school  asserts  that  a  tetrad  may 
function  as  a  diad  atom.  The  followers  of  the  first  school  maintain 
that  in  the  molecule  CO,  for  instance,  the  carbon  atom  is  tetravalent, 
but  two  of  its  affinities  are  mutually  satisfied;  the  opponents  of  this 
view  say  that  in  CO  the  carbon  atom  is  divalent,  and  that  the  other 
pair  of  bonds  is  latent.  The  dispute  has  been  wholly  a  battle  about 
words.  Whether  the  two  bonds  are  latent,  or  are  mutually  satisfied, 
as  Lessen  remarks,  'zwei  und  zwei  geben  dock  immer  vier.' 

But  if  always  existent,  are  the  bonds  always  of  equal  value  ?  Are 
the  two  pairs  of  bonds  which  hold  the  two  oxygen  atoms  to  the  carbon 
atom  in  the  molecule  CO2  equal  in  value  to  twice  the  pair  of  bonds 
by  which  one  oxygen  atom  is  held  to  a  carbon  atom  in  the  molecule 
CO? 

Now  if  we  wish  to  compare  things  we  must  have  a  standard; 
but  I  think  sufficient  facts  have  been  enumerated  to  shew  that  no 
standard  exists  in  terms  of  which  the  expression  'value  of  a  bond'  may 
be  stated.  Even  if  the  valency  of  an  atom  is  regarded  as  expressing  the 
total  number  of  parts  into  which  the  chemical  energy  of  that  atom  is 
divisible,  this  must  mean  that  the  energy  is  divisible  when  there  is  mutual 
action  between  the  given  atom  and  other  atoms  in  a  molecule.  Thus, 
assume  for  a  moment  that  the  chemical  energy  of  an  atom  of  carbon  is 
divisible  into  four  parts,  it  does  not  follow  that  each  part  represents  a 
fourth  of  the  whole  energy,  or  always  represents  the  same  portion  of 

many  free  atoms  (or  monatomic  molecules)  and  yet  for  all   practical   purposes 
behave  as  if  composed  entirely  of  diatomic  molecules. 

1  The  statement  is  sometimes  put  in  this  form ;  '  the  sum  of  the  valencies,  or 
affinities,  of  the  atoms  in  any  molecule  is  always  an  even  number.' 


CHAP.  II.  §97]  MOLECULAR  COMPOUNDS.  199 

that  energy.  To  take  an  illustration;  in  the  stable  molecule  CO  we 
must  suppose,  on  this  hypothesis,  that  the  whole  of  the  chemical  energy 
of  the  carbon  atom  is  employed  in  the  transaction  symbolised  by  the 
formula  C  —  O  ;  again,  in  the  molecule  O  —  C  —  S  the  whole  of  the  energy 
of  the  carbon  atom  is  employed,  but  the  energy  represented  by  O  -  C 
is  probably  different  from  that  represented  by  C  —  S,  and  the  sum  of 
these  is  probably  different  from  that  represented  by  the  expression 
O  —  C  —  O.  The  results  of  thermal  measurements  made  by  Thomson 
(see  par.  84,  also  post,  par.  134)  render  it  fairly  certain  that  the  quantity 
of  energy  which  changes  form  during  the  process  symbolically  expressed 
as  'linking  a  pair  of  carbon  atoms  by  a  double  bond'  bears  no  simple 
relation  to  the  quantity  of  energy  which  changes  form  when  'a  pair  of 
carbon  atoms  is  linked  by  a  single  bond.'  The  number  of  possible  ways 
in  which  the  energy  is  distributed  is,  on  this  hypothesis,  measured  by 
the  valency  of  the  atom ;  the  amount  of  the  energy  employed  in  any 
atomic  transaction  depends  on  the  nature  of  the  atom  or  atoms  between 
which  and  the  given  atom  there  is  mutual  intramolecular  action1. 

Even  if  we  adopt  this,  the  most  dynamical,  view  of  valency  that  can 
be  adopted  with  any  safety,  the  controversy  concerning  equal  and  un- 
equal bonds  is  seen  to  be  a  mere  logomachy2. 


SECTION  V.     Molecular  Compounds. 

97  In  the  preceding  sections  we  have  learned  that  some  com- 
pounds can  be  gasified  without  decomposition  while  others 
are  separated  by  heat  into  two  or  more  constituent  parts. 

The  conception  expressed  in  the  term  molecule  can  be 
applied  in  strictness  to  the  former  compounds  only,  and  the 
fundamental  notions  regarding  the  structure  of  molecules 
must  be  gained  by  the  study  of  such  gasifiable  compounds. 

1  For  a  fuller  working  out  of  this  way  of  regarding  valency  see  Claus,  Ber. 
14.  432. 

2  It  is  sometimes  said  that  the  hydrogen  atoms  in  the  molecule  of  benzene  are 
of  equal  value,  but  when  one  of  these  atoms  is  replaced  by  a  radicle  the  remaining 
five  are  of  different  values  relatively  to  the  radicle  introduced  into  the  molecule. 
To  make  such  a  statement  as  this,  it  seems  to  me,  is  to  employ  the  term  value  in 
too  loose  and  vague  a  way.     All  the  hydrogen  atoms  in  a  molecule  of  a  mono- 
derivative  of  benzene  are  monovalent,  and  therefore  of  equal  value  so  far  as 
'proportion  in  exchange'  for  chlorine,  bromine  &c.  goes.     What  appears  to  be' 
meant   by  the   statement   in   question   is,   that   more   than  one   mono-derivative 
(chloro-  bromo- or  generally  X  -  derivative)  can  be  obtained  from  the  mole- 
cule CgHjA';  but  this  is  simply  a  special  illustration  of  the  general  proposition 
that  the  properties  of  compounds  are  not  wholly  dependent  on  the  valencies  of 
their  constituent  atoms. 


2OO  ATOMIC   AND   MOLECULAR   SYSTEMS.          [BOOK  I. 

But,  it  may  be  asked,  is  there  a  distinction  of  kind,  or 
only  one  of  degree,  between  those  compounds  which  can  be 
gasified,  and  those  which  separate  into  parts  when  they  are 
heated  ?  This  question  has  been  provocative  of  much  dis- 
cussion. Kekule1  and  others  have  employed  the  term  atomic 
compounds  to  express  those  compounds  which  can  be  vaporised 
without  decomposition,  and  they  have  contrasted  these  with 
molecular  compounds,  meaning  thereby  those  compounds  which 
separate  into  two  or  more  parts  when  heated. 

This  division  of  compounds  has  played  an  important  part 
in  the  development  of  the  hypothesis  of  valency.  Kekule 
has  always  insisted  that  facts  regarding  atomic  compounds 
can  alone  be  employed  as  data  for  rinding  the  valencies  of 
elementary  atoms ;  his  opponents  have  retorted  by  de- 
manding a  definition  of  molecular  as  opposed  to  atomic 
compounds,  and  by  shewing  that  every  proposed  definition 
fails  when  applied  to  actual  phenomena. 

But  it  is  not  so  much  as  it  concerns  the  hypothesis  of 
valency  that  the  distinction  implied  in  the  words  atomic  and 
molecular  compounds  ought,  I  think,  to  be  insisted  on ;  if  the 
arguments  put  forward  in  the  preceding  section  are  of  any 
value,  we  must  agree  to  confine  what  may  be  called  the  non- 
geometrical  hypothesis  of  valency  to  gaseous  compounds. 
There  are  however  many  and  varied  phenomena,  all  more 
or  less  belonging  to  the  borderland  between  chemistry  and 
physics,  which  may  conveniently  be  considered  under  the 
heading  of  molecular  compounds. 

i  And  I  would  begin  by  admitting  that  no  strict  definition 
of  molecular,  as  opposed  to  atomic,  compounds,  can  be  given, 
which  shall  enable  us  to  assign  every  disputed  case  to  its 
proper  class.  A  substance  may  yield  a  vapour  which  is 
chemically  homogeneous  below  a  certain  temperature  but 
heterogeneous  above  this  temperature  ;  we  cannot  fix  a  limit- 
ing temperature  for  each  group  of  compounds  and  say,  that 
those  which  yield  vapours  homogeneous  above  this  tempera- 
ture are  atomic,  while  those  in  the  vapour  of  which  dissocia- 
tion begins  below  the  temperature-limit  are  molecular. 

1  See  his  Lehrbuch,  Vol.  I.  pp.  142,  145,  443,  £c. :  also  Compt.  rend.  58.  510. 


CHAP.  II.  §§98, 99]        MOLECULAR   COMPOUNDS.  2OI 

I  would  again  urge  the  importance  of  remembering  that 
when  we  say  that'  a  gas  consists  of  molecules  of  this  or  that 
composition,  we  refer  and  can  refer  only  to  the  average  com- 
position of  the  gas ;  many  molecules  may  be  dissociated  into 
two  or  more  chemically  different  kinds  of  matter,  other 
molecules  may  be  aggregated  into  complex  groups.  Even  in 
an  elementary  gas  at  moderate  temperatures  some  atoms  and 
many  groups  of  molecules  may  be  present  at  any  moment : 
the  values  obtained  for  the  specific  gravities  of  gaseous  bro- 
mine and  iodine,  and  for  gaseous  nitrogen  dioxide,  stannous 
chloride,  and  acetic  acid  well  illustrate  the  gradual  nature  of 
the  passage  from  one  average  molecular  state  to  another1. 
99  Some  chemists  would  recognise  the  existence  of  molecular 
compounds  in  mixtures  of  two  or  more  liquids,  and  in  solu- 
tions of  salts,  and  of  gases  (e.g.  CO2),  in  water.  In  such  cases 
the  proportions  in  which  the  substances  are  supposed  to  be 
combined  are  very  variable.  It  cannot  be  correct  to  speak 
of  a  molecule  of  the  mixture  of  alcohol  and  water,  or  of  a 
molecule  of  the  solution  of  salt  in  water,  although  it  may  be 
permissible  to  regard  these  liquids  as  containing  groups  of 
molecules  of  alcohol  and  water,  or  of  salt  and  water. 

As  examples  of  bodies  which  seem  to  hold  a  place  between 
definite  chemical  compounds  and  mere  mixtures  may  be  noted 
the  products  of  the  fusion  together  of  sulphur  and  selenion. 
Rathke2  fused  together  sulphur  and  selenion,  dissolved  the 
fused  mass  in  carbon  disulphide,  and  fractionally  precipitated 
by  gradual  evaporation ;  he  then  redissolved  the  various  pre- 
cipitates, and  again  fractionated.  The  precipitates  all  con- 
sisted of  monoclinic  crystals  composed  of  sulphur  and  selenion 
(neither  element  exhibiting  the  properties  which  characterise 
it  in  the  free  state)  but  varying  in  quantitative  composition 
between  the  limits  expressed  by  the  formula:;  SeS4  and  Se4S. 
Rathke  thinks  it  possible  that  elements  which  are  chemically 
very  analogous  may  combine  in  varying  proportions  to  pro- 
duce isomorphous  bodies. 

There  are  other  actions  wherein  small  changes  in  physical 

1  See  par.  99,  pp.  203,  106—7. 

s  Ber.  18.  1534.     See  also  Lehmann,  Zeitschr.f,  physikal.  Chcmie,  1.  15. 


202  ATOMIC   AND   MOLECULAR   SYSTEMS.          [BOOK  I. 

conditions  suffice  to  cause  changes  in  the  relative  quantities  of 
substances  combined  in  definite  proportions ;  for  instance, 
when  the  substance  containing  water  and  sodium  phosphate 
in  the  proportion  Na2HPO4:  I2H2O  is  heated,  it  very  readily 
loses  water  and  becomes  Na2HPO4.  7H2O.  If  by  molecular 
compound  is  meant,  a  loose  combination  in  definite  pro- 
portions of  two  or  more  chemically  different  kinds  of  matter 
so  as  to  produce  another  kind  of  matter  characterised  by 
fairly  definite  properties  but  readily  undergoing  change,  then 
we  may  certainly  say  that  Na2HPO4.  i2H2O  is  a  molecular 
compound. 

Once  more,  compounds  exist  which  are  characterised  by 
very  definite  properties,  but  which,  when  heated,  undergo 
gradual  change  into  two  or  more  substances,  the  original 
compound  being  gradually  re-formed  as  the  vapours  cool. 
Thus  the  formula  PC15  expresses  the  elementary  composi- 
tion of  an  undoubted  chemical  compound ;  when  this  solid 
substance  is  heated  it  vaporises,  but  the  vapour  can  be 
proved  by  experiment  to  contain  molecules  of  PC13  and  C12, 
along  with  undecomposed  PC15.  The  following  numbers 
shew  the  gradual  progress  of  the  change  which  occurs  : — 

Calculated  sp.  gr.  of  gaseous  PC15=7'2  IF  *        1 

gas  consisting  of  PC13  +  C12  =  3-6)  La 

Number  of  molecules 

Temperature.  Sp.  gr.  of  vapour.  decomposed *  per  too 

molecules  of  PClj. 

182°  5'08  417 

IQO  4-99  44-3 

200  4-85  48-5 

230  4-30  67-4 

250  4-00  80-0 ' 

274  3-84  87-5 

288  3-67  96-2 

300  3-65  97-3 

1  Calculated  by  means  of  the  formula  p= —= where  /= number  of 

molecules  decomposed,  D= observed  sp.  grav.  of  gas,  d=  theoretical  sp.  grav.  of 
vapour  supposing  no  dissociation  to  occur.  This  formula  assumes  that  each 
molecule  separates  into  two  parts:  if  each  molecule  separates  into  a  parts,  the 

formula  is/=-r-_  .    See  Naumann,  Lehr-  und Handbuch der  Tliermochemie, 

pp.  114,  115. 


CHAP.  II.  §99]      GASEOUS  MOLECULAR  COMPOUNDS.  203 

The  following  numbers1  representing  the  specific  gravities 
of  gaseous  nitrogen  tetroxide  at  various  temperatures  exhibit 
the  gradual  dissociation  of  molecules  of  N2O4  into  molecules 
ofNO2:— 

Texture.          Sp.  *,  of  vapou,  ^^^^ 

267°  2-65  19-96  6'5 

35-4  2-53  25-68  8-1 

39*8  2-46  29-23  iro 

49"6  2-27  40*04  1 2- 1 

60-2  2-08  52-84  13-0 

70-0  1-92  65-57  10-4 

80-6  r86  76-61  8-8 

96-0  172  84-83  1-8 

135*0  r6o  98-69 

As  N2O4  is  dark-red  and  nearly  opaque,  and  NO2  is  trans- 
parent and  nearly  colourless,  the  change  from  one  compound 
to  the  other  can  be  traced  by  observing  the  colour  of  the 
heated  gas. 

A  study  of  the  specific  gravity  of  the  vapour  obtained  by 
heating  acetic  acid,  at  different  temperatures  and  pressures, 
shews  that  the  specific  gravity  decreases  as  temperature  rises 
whether  pressure  be  small  or  great,  and  that  the  specific 
gravity  also  decreases  as  pressure  falls  whether  the  tempe- 
rature be  high  or  low;  in  other  words,  the  vapour  of  acetic 
acid  becomes  specifically  heavier  by  increasing  pressure, 
temperature  being  constant,  or  by  decreasing  temperature, 
pressure  being  constant2.  The  most  probable  molecular  ex- 
planation of  these  facts  is  to  suppose  that  the  vapour  of  acetic 
acid  at  low  temperatures  contains  molecules,  or  molecular 
groups,  the  parts  of  which  hold  together  throughout  small 
temperature-intervals,  and  that  these  molecules,  or  groups, 

1  Naumann,  loc  cit.  p.  117. 

-  See  Ramsay  and  Young,  C.  S.  Journal,  Trans,  for  1886.  790  (s.  also 
Book  II.).  Comparing  the  variations  in  the  specific  gravities  of  the  vapours  of 
acetic  acid,  alcohol,  and  ether,  Ramsay  and  Young  (Phil,  Mag.  (5)  23.  129) 
found  that  the  specific  gravities  of  alcohol  vapour  and  ether  vapour  increase  as 
temperature  falls  until  a  certain  point  is  reached  beneath  which  the  specific 
gravities  are  unchanged.  They  conclude  that  the  increase  in  the  specific  densities 
of  the  vapours  of  alcohol  and  ether  are  probably  due  to  the  cohesion  of  the 
molecules,  and  not  to  the  formation  of  groups  of  molecules. 


204  ATOMIC   AND   MOLECULAR   SYSTEMS.          [BOOK  I. 

are  heavier  than  those  which  compose  the  vapour  of  the  same 
acid  at  temperatures  considerably  above  the  boiling  point  of 
the  compound. 

If  we  define  a  molecular  compound  to  be  one  the  mole- 
cules of  which  may  exist  in  the  gaseous  state  at  low  tempe- 
ratures but  are  gradually  decomposed  into  less  dense  mole- 
cules of  the  same  kind  of  matter  as  temperature  rises,  then 
we  must  regard  acetic  acid  at  temperatures  not  far  above  its 
boiling  point  as  a  molecular  compound. 

But  if  this  is  so,  we  evidently  have  a  series  of  substances, 
beginning  with  solutions  of  salts  or  gases  in  water,  and 
proceeding  through  crystallised  solid  salts  to  acetic  acid 
vapour  at  low  temperatures,  which  connects  mechanical  mix- 
tures on  the  one  hand  with  stable  gaseous  compounds  on  the 
other. 

It  might  be  urged  that  we  ought  not  to  distinguish  be- 
tween the  particles  which  compose  acetic  acid  vapour  at  low 
temperatures  and  those  which  form  the  vapour  of  the  same 
acid  at  high  temperatures  ;  that  if  a  molecule  is  '  that  small 
part  of  a  gas  the  parts  of  which  do  not  part  company  during 
the  motion  of  agitation  of  the  gas,'  then  the  reasoning  which 
compels  us  to  say  that  the  molecule  of  acetic  acid  vapour  at 
220°  is  represented  by  the  formula  C2H4O2,  likewise  compels 
us  to  say  that  at  120°  the  molecule  of  this  gas  is  represented 
by  the  formula  C3H6O3  (pressure  in  each  case  being  760  mm.). 
The  statement  that  acetic  acid  at  low  temperatures  is  a  mole- 
cular compound  does  not  appear  to  me  to  go  against  this 
reasoning  ;  for  this  statement  only  implies  that  at  low  tempe- 
ratures the  vapour  of  this  acid  is  composed  of  particles,  of 
varying  masses — which  may  be  called  molecules  or  mole- 
cular groups — but  that  as  temperature  rises  these  all  tend  to 
separate  into  particles  whose  composition  is  represented  by  the 
formula  C2H4O2.  The  particle  having  the  composition  C2H4O2 
is  stable  throughout  so  large  a  range  of  temperature  that  we 
may  apply  to  it  and  to  it  only  the  knowledge  we  have  gained 
regarding  the  structure  of  molecules.  It  is  better  not  to 
apply  the  term  molecule  to  the  heavier  particles,  (i)  because 
they  so  readily  separate  into  lighter,  and  comparatively  stable, 


CHAP.  II.  §99]       GASEOUS  MOLECULAR  COMPOUNDS.  2O5 

particles ;  (2)  because  what  we  know  of  molecular  structure 
has  been  gained  from,  and  can  only  be  strictly  applied  to, 
the  study  of  molecules  which  are  stable  throughout  a  con- 
siderable range  of  temperature;  and  (3)  because  by  re- 
cognising the  possibility  of  the  existence  in  certain  vapours 
of  groups  of  molecules,  which  are  not  mere  mixtures  but  on 
the  other  hand  are  not  to  be  classed  as  true  molecules,  we 
have  the  means  of  explaining,  in  a  general  way,  many  phe- 
nomena which  at  present  cannot  be  explained  by  any  other 
equally  simple  hypothesis  which  is  in  keeping  with  the  funda- 
mental conceptions  of  the  molecular  theory  of  matter. 

That  the  existence  of  molecular  groups  in  a  gas  at  low  tem- 
peratures is  in  keeping  with  this  theory  can  readily  be  shewn. 
When  two  gases  are  at  equal  temperatures  the  mean  kinetic 
energy  of  agitation  of  the  molecules  must  be  the  same  in 
both  ;  but  although  the  mean  kinetic  energy  is  constant  for  a 
given  temperature,  yet  the  kinetic  energy  (and  hence  the 
temperature)  of  many  molecules  may  differ  from  this  mean 
value.  If  the  temperature  of  the  gas  is  increased,  there  is  an 
increase  not  only  of  the  energy  of  agitation  of  the  molecules 
as  a  whole,  but  also  of  the  energy  due  to  the  internal  motions 
of  the  parts  of  each  molecule ;  as  the  latter  energy  increases, 
a  point  is  reached  at  which  the  molecule  decomposes  into 
its  constituent  parts,  but  these  may  again  unite  in  some  other 
portion  of  the  mass  of  gas.  As  temperature  continues  to  rise 
a  point  will  come  at  which  molecular  decompositions  and  re- 
compositions  are  equal  in  unit  of  time ;  the  temperature  at 
which  this  state  of  matters  is  reached  has  been  called  (by 
Naumann  and  others)  the  decomposition-temperature;  from 
this  point  onwards,  as  temperature  rises,  the  molecular  de- 
compositions will  exceed  the  recompositions,  until  finally 
there  are  no  recompositions,  or  these  are  so  few  in  number 
that  the  average  state  of  the  gas  is  fitly  described  as  that 
of  complete  decomposition. 

Now  if  we  suppose  that  the  vapours  coming  from  certain 
liquids,  especially  from  dissociable  compounds,  at,  or  near  to, 
their  boiling  points  consist  to  a  great  extent  of  molecular 
aggregations,  we  may  trace  the  gradual  decomposition  of 


2O6  ATOMIC   AND   MOLECULAR  SYSTEMS.          [BOOK  I. 

these  aggregates  into  true  gaseous  molecules,  just  as  we  have 
traced  the  decomposition  of  molecules  of  one  kind  of  matter 
into  those  of  another  kind  of  matter.  Many  spectroscopic 
facts  almost  necessitate  the  assumption  that  groups  of  mole- 
cules may  exist,  and  behave  for  certain  small  changes  in 
physical  conditions  as  definite  wholes1. 

But  it  might  be  asked,  why  should  not  all  molecules 
decompose  when  heated  ?  It  is  extremely  probable  that  all 
molecules  are  capable  of  being  decomposed  by  heat.  The 
results  of  Meyer's  experiments  on  iodine  vapour  shew  that 
the  diatomic  molecules  of  this  gas  are  separated  into  atoms 
at  high  temperatures.  The  following  table  exhibits  the 
process  of  change  from  I2  to  I. 

Dissociation  of  Iodine  molecules^. 


Temp. 

448° 
680 

Sp.  gr.  of 

vapour. 

874 

Percentage        Rise  of           Increase  in 
decomposition.       temp.         de?omSkfon. 

Mean  increase 
in  decomposition 
for  ioo3. 

764 

8-28 

855 
940 

8-07 
7-60 

8-6 
H'SJ 

85°  

.      IO3     .. 

10*5 

6-9 

IO'2 

1043 

•  (I275 
(approxi-l 

mately)  US 

7'01 
5-82 

5-06 

25-0  ' 

5O*  ^  ' 

66-2J  ' 
73-ri  ' 

J      

232  
78  

25-5  .... 
157  .... 

..  6-9  .... 

iro 

137 
8-8 

Somewhat  similar  results  have  been  obtained  with  bromine. 
A  fact  of  much  interest  is  disclosed  by  studying  the  specific 
gravities  of  gaseous  bromine  and  chlorine  at  low  and  at  high 
temperatures ;  some  of  the  results  of  such  a  study  are  given 
in  the  following  table3. 

1  In  connexion  with  this  subject  see  especially  the  article  'Constitution  of 
bodies,'  by  Clerk  Maxwell,  in  the  Encyclopedia  Briiannica.  (pth  Ed.)  See  also 
'Report  of  the  B.  A.  Committee  on  Spectrum  Analysis.'  Brit,  Ass.  Reports  for 
1880,  2581  et  seq.  See  especially  pp.  284—298.  Also  the  article  'Aggregation, 
States  of  in  the  new  edition  of  Watts'  Dictionary  of  Chemistry. 

8  Naumann,  Ber.  13.  1050,  using  the  numbers  of  Crafts  and  Meier,  do.  do.  868. 

3  Jahns,  Ber.  15.  1238. 


CHAP.  II.  §§  99>  1 00]    GASEOUS  MOLECULAR  COMPOUNDS.      2O/ 
Specific  gravities  of  gaseous  Bromine  and  Chlorine. 

Temp,  measured  in  degrees  above  Snerifir  irravi'tv  Deviation  of  sp.  gr.  from  normal, 

boiling  point  of  in  per  centages  of  latter. 


IROMINE. 

CHLORINE. 

BROMINE. 

CHLORINE. 

BROMINE. 

CHLORINI 

40° 

40° 

57HS 

2-4844 

3-38I 

I  '397 

60 

60 

5-6809 

2*4810 

2-872 

1*261 

80 

80 

5-6503 

2-4776 

2-223 

ri22 

IOO 

IOO 

5-6197 

2-4742 

1719 

0-984 

120 

120 

5-589I 

2-4708 

1*650 

0-845 

160 

160 

5-5279 

2-4641 

0-058 

0*571 

2OO 

2-4572 

0-290 

240 

2-4504 

O'OOO 

We  have  here  a  phenomenon  very  analogous  to  that  pre- 
sented by  acetic  acid ;  and  if  an  analogous  explanation  is  to 
be  given,  we  must  suppose  that  bromine  vapour  at  tem- 
peratures from  40  to  140  degrees  above  the  boiling  point  of 
this  substance  contains  molecular  groups  which  are  slowly 
decomposed  as  temperature  increases ;  and  that  the  same 
holds  good  of  chlorine  vapour,  only  that  in  this  case  the 
molecular  groups  are  relatively  lighter,  but  more  stable  as 
regards  heat,  than  those  of  bromine. 

A  study  of  the  specific  gravities  of  the  gases  obtained  by 
heating  various  liquid  compounds  shews  that  in  very  many 
cases  the  specific  gravity  decreases  as  the  temperature  rises, 
and  that  a  constant  value  is  not  obtained  until  the  gas  has 
been  heated  many  degrees  above  the  boiling  point  of  the 
liquid. 

Facts  have  now  been  recounted  sufficient  I  think  to 
warrant  the  adoption  of  the  hypothesis  that  gaseous  mole- 
cules may  hold  together  in  groups,  the  members  of  which 
do  not  part  company  throughout  more  or  less  extended 
ranges  of  temperature  and  pressure  ;  and  if  this  is  so  in  gases, 
much  more  should  we  expect  to  find  the  existence  of  mole- 
cular groups  in  liquids  and  solids. 

100  The  hypothesis,  by  the  application  of  which  we  hope  to 
find  many  groups  of  facts  falling  into  some  kind  of  order, 
may  be  broadly  stated  as  consisting  in  the  recognition  of  a 
third  order  of  particles  more  complex,  but  less  stable,  than 
;tsthe  molecule,  as  the  molecule  is  more  complex,  but  less 
--table,  than  the  atom.  This  hypothesis  affords  no  definition 


2O8  ATOMIC   AND   MOLECULAR   SYSTEMS.          [BOOK  I. 

of  the  third  order  of  particles,  nor  does  it  always  enable  us  to 
refer  a  special  case  to  this,  or  that,  order  of  particles.  It  is  a 
general  guide  and  as  such  only  must  it  be  employed. 
101  Many  salts  when  in  solution  undergo  changes  not  so 
marked  as  those  usually  called  chemical,  and  yet  too  definite 
to  be  altogether  classed  as  physical.  Thus  an  aqueous  so- 
lution of  ferric  chloride  undergoes  partial  separation  into 
hydrochloric  acid  and  a  colloidal  form  of  ferric  hydrate ; 
aqueous  solutions  of  various  alums  are  partially  separated 
into  their  constituents  when  heated.  The  direction  of  many 
of  these  changes  may  be  partially  reversed  by  altering  the 
conditions  of  temperature1.  Again  hydrated  cobalt  chloride 
crystallises  in  a  rose-red  form  (CO2C14  .  I2H2O),  while  the 
colour  of  the  dehydrated  crystals  (CO2C14)  is  blue ;  if  an 
aqueous  solution  of  the  red  salt  is  warmed,  the  colour  slowly 
becomes  darker  and  finally  changes  to  blue,  but  the  rose 
red  colour  gradually  reappears  as  the  liquid  cools.  The 
temperature  at  which  the  change  from  hydrated  to  dehydrated 
salt  occurs  is  the  lower,  the  less  the  amount  of  water  present 
relatively  to  that  of  salt.  A  crystal  of  cobalt  chloride  grow- 
ing in  a  blue-coloured  solution  is  seen  under  the  microscope 
to  be  surrounded  by  a  film  of  pink  liquid,  which  indicates 
the  existence  round  the  crystal  of  a  zone  of  liquid  containing 
relatively  less  of  the  salt  than  the  rest  of  the  solution2. 

From  the  results  of  Lehmann's  microscopic  studies3  on  the 
formation  of  crystals  of  hydrated  ferrous  chloride,  cobaltous 
chloride,  and  cupric  chloride,  it  appears  certain  that  an  aqueous 
solution  of  one  of  these  salts  from  which  crystals,  now  of 
a  more  hydrated  and  now  of  a  less  hydrated  salt,  separate,  as 
temperature  varies,  does  not  contain  at  a  fixed  temperature 
only  the  one  hydrate  and  at  another  temperature  only  the 
other  hydrate.  As  temperature  slowly  rises  the  molecular 
groups  tend  to  fall  to  pieces  and  so  the  liquid  becomes  poorer 
in  particles  of  the  relatively  most  hydrated  salt ;  on  cooling, 

1  The  expresssion  '  dissociation  of  salts  in  solution '  is  sometimes  applied  to 
these  processes.     See  Book  II. 

2  See  Lehmann,  Zeitschr.fiir  Krystallog.  1.  99. :  see  also  Potilitzin,  Ber.  17.  276. 

3  Zeitschr.  fiir  Krystallog.  1.  100 — 103. 


CHA1MI.§  101]        MOLECULAR  COMPOUNDS.  2OQ 

the  conditions  are  reversed,  and  the  liquid  becomes  poorer  in 
particles  of  the  least  hydrated  salt.  Lehman n  considers  the 
three  cases  ;  (i)  the  liquid  is  equally  saturated  for  the  hydrate 
rich  in  water  and  for  that  poorer  in  water;  (2)  the  liquid  con- 
tains rather  more  of  one  hydrate  than  of  the  other;  (3)  the 
liquid  is  concentrated  as  regards  one  hydrate,  but  dilute  as 
regards  the  other.  He  shews  that,  as  temperature  slowly 
increases,  in  the  first  case  crystals  of  both  hydrates  grow 
simultaneously  and  at  the  same  rate  until  the  spheres1  of  the 
crystals  touch,  when  growth  is  almost  entirely  stopped  ;  in 
the  second  case  both  kinds  of  crystals  grow,  but  for  a  time 
one  kind  grows  more  quickly  than  the  other,  then  both  grow 
at  the  same  rate,  and  then  the  second  kind  of  crystals  grow 
more  rapidly  than  the  first ;  in  the  third  case  those  crystals 
which  are  present  in  the  liquid  in  greater  quantity  grow 
rapidly,  and  the  others  dissolve  rapidly,  so  that  the  dissolving 
crystals  appear  to  pass  directly  into  crystals  of  the  other  hydrate. 

The  definite  form,  solubility,  temperature  of  formation,  &c. 
of  each  kind  of  crystal  formed  in  these  experiments  conducted 
by  Lehmann  prevent  us  from  regarding  the  various  crystalline 
solids  as  mere  mixtures  of  ice  and  salt ;  on  the  other  hand, 
the  extremely  small  variations  in  temperature,  or  in  the  re- 
lative quantities  of  water  and  salt,  required  to  cause  change 
from  one  crystal  to  another,  equally  prevent  us  from  attempt- 
ing to  explain  the  properties  of  each  hydrate  as  wholly,  or 
almost  wholly,  conditioned  by  the  mutual  interactions  of 
atoms  forming  the  molecule:  we  seem  forced  to  adopt  the 
hypothesis  of  molecular  compounds. 

Several  compounds  exist  each  in  more  than  one  modifi- 
cation, one  form  being  generally  more  stable  towards  heat 
than  the  other.  A  typical  case  of  this  kind  is  presented  by 
antimonious  iodide,  SbI3 ;  this  compound  crystallises  in  red 
hexagonal  forms  which  are  suddenly  changed  at  1 14°  to  an 
aggregation  of  yellow  orthorhombic  crystals,  the  original 
external  form  of  the  mass  being  preserved2. 

1  Lehmann's  term  is  'der  Hof  des  Krystalles:''  each  crystal,  he  says,  can  be 
seen  under  the  microscope  to  be  surrounded  by  a  liquid  film,  from  which  it  draws 
Us  supplies  of  solid  matter;  this  is  the  Ifofor  sphere  of  the  crystal. 

2  J.  P.  Cooke,  Proe.  Anu-r.  Acad.  of  AHs  and  Sci.  [2].  5.  72. 

M.  C.  14 


2IO  ATOMIC  AND   MOLECULAR  SYSTEMS.         [BOOK  I. 

Several  carbon  compounds  (apparently  all  belonging  to 
the  class  of  benzenoid  compounds)  exist  in  more  than  one 
form,  each  modification  being  characterised  by  a  definite 
melting  point  and  generally  also  by  a  special  crystalline  form. 
Thus  chlorodinitrobenzene,  C(,H3C1(NO2)2  [i  :  2  .'4],  is  said  to 
form  monoclinic  crystals  which  melt  at  36°,  and  also  rhombic 
crystals  which  melt  at  39°.  Anthracene,  C14H10,  crystallises 
in  monoclinic  plates  melting  at  213°  which  are  easily  oxidised 
by  the  action  of  nitric  acid  to  anthraquinone  (C14H8O2)  ;  when 
a  solution,  in  benzene,  of  anthracene  is  exposed  to  sunlight 
small  prismatic  crystals  separate,  melting  at  244°,  having  the 
composition  C14H:o,  but  not  acted  on  by  nitric  acid,  and  not 
oxidised  to  anthraquinone  by  chromic  acid1.  A  very  re- 
markable instance  of  the  phenomenon  under  consideration  is 
presented  by  the  derivative  of  diphenyl  to  which  the  formula 
(C6H3BrNHCOC6H5)2  is  assigned.  This  compound  melts  at 
195° ;  if  the  melted  substance  is  cooled  quickly  and  again 
heated  its  melting  point  is  now  99° ;  but  if  heating  is  con- 
tinued the  liquid  again  solidifies  at  125 — 130°,  and  the  solid 
thus  obtained  melts  once  more  at  195°.  Finally  if  the  solid 
which  melts  at  195°  is  raised  to  that  temperature  and  then 
slowly  cooled,  the  product  possesses  the  normal  melting  point2, 
viz.  195.  When  a  substance  crystallises  in  more  than  one 
system,  one  crystalline  form  frequently  approaches  as  nearly 
as  possible  to  the  other ;  one  form  may  be  said  to  imitate  the 
other  both  crystallographically  and  optically3;  thus  arsenious 
oxide  crystallises  in  regular  octahedra  and  also  in  rhombic 
prisms,  the  latter  exhibiting  an  angle  identical  with  the  angle 
of  the  regular  octahedron. 

O.  Lehmann4  has  collected  and  discussed  many  instances 
of  the  exhibition  of  different  physical  properties  by  com- 
pounds possessing  the  same  elementary  composition5.  The 

1  See  Armstrong  and  Groves,  foe.  cit.  p.  199. 

2  See  E.  Lellmann,  Ber.  15.  2835. 

3  Pasteur,  Ann.  Chim.  Phys.  [3]  23.  267. 

4  Zeitschr.  fur  Krystallog.  1.  97.     See  also,  in  connexion  with   the  subject 
generally,  the  article   'Isomerie,   physikalische '  in  Neues  Haudivorterbtuh  der 
Chemie,  Bd.  in.  pp.  836—843. 

8  On  this  subject  see  also  Laubenheimer,  Ber.  9.  760. 


CHAP.  II.§IOl]  PHYSICAL   ISOMERISM.  211 

phenomenon,  which  may  be  called  physical  isomerisin1,  pre- 
sents analogies  with  allotropy  (see  ante,  par.  67);  in  both, 
temperature  is  the  most  important  condition  affecting  the 
change  from  one  form  to  another,  and  this  change  is  accom- 
panied in  both  classes  of  phenomena  by  disappearance  or 
production  of  heat. 

Lehmann  divides  physically  isomeric  bodies  into  two 
classes:  (i)  those  in  which  change  from  one  form  to  another 
occurs  at  a  definite  temperature,  the  direction  of  the  change 
being  dependent  on  very  small  differences  of  temperature; 
(2)  those  which  exhibit  two  forms,  one  more  stable  than  the 
other,  and  in  which  change  from  one  form  to  the  other  does 
not  occur  at  a  definite  temperature,  and  is  not  reversible  by 
heat  alone. 

Ammonium  nitrate  is  an  example  of  a  substance  belong- 
ing to  the  first  class  ;  the  rhombic  crystals  of  this  salt,  which 
separate  at  ordinary  temperatures  from  an  aqueous  solution, 
melt  at  (about)  168°;  as  the  molten  mass  cools  crystals  be- 
longing to  the  regular  system  are  formed,  but  at  (about) 
125°  these  change  to  rhombohedral  forms  ;  at  (about)  87°  the 
rhombohedral  forms  are  converted  into  rhombic  needles, 
from  which,  at  36°  or  so,  the  original  rhombic  crystals  are 
produced.  If  the  rhombic  crystals  are  again  slowly  heated 
the  rhombic  needle-shaped  crystals  form  at  (about)  36° ;  the 
rhombohedral  forms  appear  at  (about)  87°;  the  regular 
crystals  at  (about)  125°;  and  finally  the  solid  melts  at  198°. 
Again,  if  a  little  sulphur  is  melted  on  a  microscopic  slide, 
under  a  cover,  and  the  slide  is  arranged  so  that  temperature 
can  be  easily  regulated2  monoclinic  crystals  are  produced, 
but  as  temperature  falls  these  change  into  rhombic  forms ; 
it  is  possible  to  regulate  the  temperature  so  that  definite 
amounts  of  each  form  exist  simultaneously,  but  on  the 
slightest  change  of  temperature  the  rhombic  crystals  grow  at 
the  expense  of  the  monoclinic,  or  vice  versa. 

The   behaviour   of  dibromopropionic   acid   when   heated 

1  The  term  physical  isomerism  seems  to  have  been  first  used  by  L.  Carius, 
Annalen,  126.  214  (see  also  do.  130.  237). 

s  Lehmann  describes  an  apparatus  for  this  purpose  (loc.  cit.  pp.  102 — 3). 

14—2 


212  ATOMIC   AND   MOLECULAR   SYSTEMS.          [BOOK  I. 

illustrates  the  nature  of  the  changes  which  characterise  sub- 
stances belonging  to  Lehmann's  second  class  of  physical 
isomerides.  This  substance  crystallises  in  rhombic  forms 
which  melt  at  (about)  64°;  if  the  molten  mass  is  heated  a 
few  degrees  above  this  point  the  same  rhombic  crystals 
are  again  produced  on  cooling;  but  if  the  molten  substance 
is  heated  many  degrees  above  64°  and  is  then  allowed  to 
cool,  small  flat  nearly  right-angled  tables  are  obtained 
which  melt  at  (about)  51°.  If  the  less  stable  form  melting  at 
51°  is  slowly  heated  growth  of  the  other  and  more  stable 
crystals  is  noticed  under  the  microscope ;  the  growth  at  first 
is  rapid,  then  slower,  but  before  the  change  has  gone  far  the 
melting  point  of  the  less  stable  crystals  is  reached  and  the 
whole  mass  becomes  liquid.  If  the  more  stable  form  is 
melted,  heated  some  degrees  above  64°,  and  is  then  brought 
into  contact  with  crystals  of  both  forms,  growth  of  each 
modification  proceeds  until  the  crystals  touch,  after  which 
the  more  stable  (higher  melting)  crystals  grow  into  the  others 
until  the  latter  are  completely  changed  into  the  stabler  forms. 

Another  instance  of  Lehmann's  second  class  is  furnished 
by  paranitrophenol.  This  compound  crystallises  from  hot 
aqueous  solutions  in  monoclinic  crystals,  and  from  cold 
aqueous  (or  alcoholic)  solutions  in  crystals  belonging  to  the 
same  system  but  differing  in  form  and  melting  point  from 
the  others.  By  fusing  either  form  and  allowing  the  molten 
mass  to  cool,  only  the  less  stable  (lower  melting)  crystals 
are  produced;  but  if  a  little  of  the  substance  is  melted  on  a 
microscopic  slide;  and  a  crystal  of  the  second  (stabler)  form 
is  placed  in  contact  with  the  edge  of  the  solidified  mass, 
and  heating  is  then  again  commenced,  crystals  of  the  stabler 
form  begin  to  grow  at  the  expense  of  the  other  crystals,  at 
first  rapidly  and  then  more  slowly,  until  both  forms  melt,  the 
less  stable  at  a  lower  temperature  than  the  more  stable. 

Substances  of  which  ammonium  nitrate  is  the  type  ap- 
pear to  be  less  profoundly  modified  by  the  action  of  heat 
than  substances  belonging  to  the  class  represented  by  dibromo- 
propionic  acid.  Substances  belonging  to  the  first  of  these 
classes  shew  analogies  with  many  of  the  molecular  com- 


CHAP.  II.  §  101]  PHYSICAL   ISOMERISM.  213 

pounds  discussed  in  the  present  section  ;  compare  e.  g.  the 
action  of  heat  on  hydrated  cobalt  salts,  with  the  action  of 
the  same  agent  on  dibromopropionic  acid  or  on  paranitro- 
phenol.  Moreover  the  course  of  the  change  brought  about 
by  the  action  of  heat  on  these  bodies  shews  some  analogies 
with  the  processes  of  gaseous  dissociation.  For  these  rea- 
sons Lehmann  has  summarised  the  phenomena  characteristic 
of  bodies  of  this  class  under  the  term  physical  polymerism, 
and  the  phenomena  characteristic  of  bodies  of  the  other  class 
under  the  term  physical  metamerism.  The  former  term  im- 
plies that  the  physically  different  forms  exhibited  by  a  sub- 
stance belonging  to  this  class  are  to  be  regarded  as  associ- 
ated with  the  existence  of  physical  molecules,  each  formed 
by  the  grouping  together  of  a  different  number  of  chemical 
molecules  (as  defined  in  Chap.  I.  par.  13,  p.  26).  The  term 
physical  metamerism  on  the  other  hand  implies  that  the 
physical  molecule  of  each  different  form  of  a  substance 
belonging  to  this  class  is  composed  of  the  same  number  of 
chemical  molecules,  but  that  the  arrangement  of  these  is 
different  in  each  case. 

Lehmann's  classification  is  certainly  based  on  no  fanciful 
analogies.  Pclymerism  and  metamerism  are  well  marked 
phenomena  among  gaseous  molecules ;  and  the  hypothesis  of 
the  existence  of  groups  of  molecules  characterised  by  definite 
properties,  but  each  of  which  groups  is  readily  decomposed 
by  heat,  appears  to  be  as  simple  as  any  other  molecular  and 
atomic  hypothesis  that  can  be  proposed  to  explain  the 
observed  facts.  But  the  analogy  between  the  reactions  of 
gaseous  molecules  and  the  changes  undergone  by  solid  and 
liquid  substances  may  be  pushed  too  far;  we  ought  to  recog- 
nise how  small  and  inexact  our  knowledge  is  of  the  mole- 
cular actions  of  the  latter  classes  of  bodies.  Qualification 
of  the  terms  molecule,  polymerism,  and  metamerism,  by  the 
adjective  physical,  widens  the  meanings  of  these  terms  by 
making  them  applicable  to  a  larger  class  of  phenomena,  but 
at  the  same  time  it  makes  the  application  less  precise1. 

1  Lehmann   considers   in   considerable   detail   the   phenomena  attending   the 
change  of  one  form  of  a  substance  into  another;   he  divides  the  changes  into 


214  ATOMIC   AND   MOLECULAR   SYSTEMS.          [BOOK  I. 

The  researches  of  Graham  on  colloidal  and  crystalloidal 
substances  are  of  the  utmost  importance  as  regards  the 
hypothesis  we  are  considering ;  to  understand  the  import- 
ance of  Graham's  work  it  is  necessary  carefully  to  study  the 
whole  series  of  papers  on  liquid  diffusion  which  he  communi- 
cated to  the  Royal  Society1.  Graham2  found  that  certain 
substances  when  in  solution  pass  very  quickly  through  wet 

groups,  according  as  both  forms  are  solid,  or  one  solid  and  one  liquid,  £c.  As  the 
subject  is  important  I  give  a  brief  resume  of  some  of  Lehmann's  results  in  this 
note,  but  the  original  paper  ought  to  be  studied  by  all  who  are  interested  in  the 
subject. 

A.  Change  of  one,  more  complex,  solid  form  of  isomeride  to  another,  less 
complex,  solid  form,  attended  with  disappearance  of  heat;  physical  mole- 
cules of  both  kinds  are  present  simultaneously,  but  at  a  certain  tempera- 
ture change  will  occur.     If  one  modification  is  heated  alone,  the  normal 
temperature    of   change   may  be    largely   exceeded    without    a    complete 
change   to   the   second    modification,    but    at    such    a    high    temperature 
contact  with  the  second  modification  may  determine  sudden  and  complete 
change. 

B.  Change  of  solid  form  to  liquid  form,  occurring  with  disappearance  of  heat 
at  a  definite  temperature  dependent  on  the  pressure ;  the  change  will  not 
be  complete,  as  molecules  of  both  kinds  will  exist  together.     If  the  specific 
gravity  of  the  solid  form  is  greater  than  that  of  the  liquid  form,  then  on 
heating  past  the  melting  point  there  will  be  rapid  expansion  as  the  physical 
molecules  of  the  solid  form  are  separated  into  those  of  the  liquid;  this  will 
be  followed  by  a  slower  regular  expansion.     If  the  specific  gravity  of  the 
solid  is  less  than  that  of  the  liquid,   expansion  will   be  small,  or  even 
negative,  until  a  point  of  maximum  density  is  reached,  after  which  expan- 
sion will  proceed  at  the  normal  rate. 

In  some  cases  a  solid  form  is  changed,  by  the  action  of  heat,  into  a 
liquid  form,  which,  at  a  higher  temperature,  is  again  changed  into  a  second 
solid  form;  e.g.  when  selenion  is  heated  till  it  becomes  viscous  and  is  kept 
at  this  temperature  for  some  time  it  changes  into  a  crystalline  form.  So  in 
the  change  of  yellow  to  red  phosphorus  by  the  action  of  heat ;  in  this  case 
it  is  probable  that  the  molecules  which  form  the  liquid  phosphorus  are  kept 
apart  for  some  time,  by  the  energy  added  as  heat  acting  against  cohesion, 
and  so  are  allowed  to  re-arrange  themselves  in  loose  groups. 

C.  Change  of  liquid  to  solid,  modification  is  complex ;  a  few  crystals  form 
and  determine  the  crystallisation  of  the  whole  mass;   in  some  cases  the 
liquid,  especially  if  viscous,  may  be  cooled  below  the  temperature  at  which 
crystallisation  normally  begins,  and  may  then  pass  into  an  amorphous  solid 
form. 

1  Happily  Graham's  papers  have  been  collected  and  published  by  the  late 
Drs  Angus  Smith  and  James  Young. 
-  Phil.  Tram,  for  1861.  185. 


CHAP.  II.§IOl]          MOLECULAR   COMPOUNDS.  215 

animal  or  vegetable  membranes,  while  others  are  scarcely,  if 
at  all,  diffusible  through  the  same  septa.  The  more  diffu- 
sible bodies  Graham  called  crystalloids,  the  less  diffusible  he 
called  colloids.  Colloidal  substances  e.  g.  albumen,  hydrated 
alumina  or  stannic  oxide,  &c.  are  very  inert  chemically  consi- 
dered, but  at  the  same  time  they  are  affected  by  the  smallest 
changes  in  their  environment,  e.g.  slight  alterations  of  tem- 
perature cause  marked  changes  in  their  properties ;  they  are 
easily  permeated  by  diffusible  crystalloidal  substances,  to 
which,  says  Graham,  they  give  up  water,  'molecule  by  mole- 
cule'; "their  existence  is  a  continual  metastasis."  Ice,  which 
under  ordinary  conditions  of  formation  is  crystalloidal,  when 
formed  in  contact  with  water  at  o°  possesses  those  properties 
which  characterise  colloids  :  "  Can  any  facts,"  says  Graham, 
"  more  strikingly  illustrate  the  maxim  that  in  nature  there 
are  no  abrupt  transitions,  and  that  distinctions  of  class  are 
never  absolute  ?" 

The  marked  differences  between  the  properties  of  colloids 
and  crystalloids  are  associated,  in  the  opinion  of  Graham, 
with  differences  of  molecular  structure.  He  regarded  the 
reacting  unit  of  a  colloid  as  probably  formed  by  the  coales- 
cence of  a  large  number  of  molecules ;  hence  the  marked 
instability,  and  at  the  same  time  the  chemical  inertness, 
which  characterise  the  class  of  colloidal  substances. 

Hittorf1  has  shewn  that  when  a  concentrated  aqueous 
solution  of  cadmium  iodide  is  electrolysed,  more  iodine  is 
separated  at  the  positive  pole  than  could  be  the  case  were 
the  composition  of  the  body  undergoing  electrolysis  repre- 
sented by  the  formula  CdI2.  Hittorf  suggests  that  the  solu- 
tion in  question  contains  molecular  groups  of  the  composi- 
tion Cd3Ie,  and  that  these  are  separated  by  the  electric  cur- 
rent into  Cd  and  Cd2I6. 

Some  interesting  observations  have  been  made  by  van 
Bemmelen2  on  the  absorption  of  acids  and  salts  by  hydrated 
oxides.  When  the  hydrated  dioxide  of  tin,  silicon,  or  man- 
ganese, is  shaken  with  an  aqueous  solution  of  a  mineral  acid, 

1  Pogg.  Ann.  106.  337,  513. 

2  7-  fiirprakt.  CAerniefr]  23.  324;  see  also  26.  227. 


2l6  ATOMIC   AND   MOLECULAR   SYSTEMS.          [BOOK  I. 

or  of  a  salt  such  as  potassium  sulphate  or  sodium  chloride,  a 
definite  quantity  of  the  acid  or  salt  is  absorbed  by  the  oxide; 
the  amount  absorbed  is  dependent  on  the  nature  of  the 
hydrated  oxide  and  that  of  the  acid  or  salt,  on  the  relative 
masses  of  oxide,  acid,  or  salt,  and  on  the  amount  of  water 
present.  The  substances  which  exhibit  this  absorptive 
action  are  characterised  by  the  readiness  with  which  the 
change  from  hydrated  to  dehydrated  oxide  and  vice  versa 
occurs;  thus  the  hydrates  SnO2.;rH2O,  SiO2.^H2O,  and 
MnO2.^'H2O,  part  with  water  when  placed  over  sulphuric 
acid,  and  the  oxides  absorb  water  when  placed  in  a  moist 
atmosphere.  The  amount  of  water  absorbed  by  any  one  of 
the  dehydrated  oxides  depends  in  part  on  its  physical  state ; 
if  the  oxide  is  strongly  heated  it  absorbs  less  water  than  if 
dried  over  sulphuric  acid  in  vactto1 ;  the  'looser'  the  aggrega- 
tion of  the  particles,  the  greater  the  quantity  of  water  ab- 
sorbed by  the  oxide. 

In  some  cases,  e.g.  the  hydrate  SiO2<4H2O,  the  amount 
of  acid  or  salt  withdrawn  from  an  aqueous  solution  was 
found  to  be  equivalent  to  the  amount  of  water  removed 
from  the  hydrated  oxide  by  drying  it  over  sulphuric  acid  in 
vacua.  In  other  cases,  e.g.  SnO2.3H2O,  3SnO2.  7H2O, 
2SnO2.3H2O,  2MnO2.5H2O,  MnO2.2HaO,  the  amount  of 
acid  or  salt  withdrawn  by  the  hydrate  from  solution  was 
greater  than  the  quantity  equivalent  to  the  loosely-held 
water  of  the  hydrate.  As  the  amount  of  water  which  some 
of  these  oxides  absorb  from  a  moist  atmosphere  was  found  to 
vary  with  the  physical  aggregation  of  the  oxide,  so  the 
amount  of  salt  or  acid  absorbed  by  these  hydrated  oxides 
was  found  to  shew  analogous  variations :  this  is  specially 
worked  out  in  detail  by  van  Bemmelen  for  the  action  of 
metastannic  acid  on  aqueous  solutions  of  HC1,  H2SO4,  KC1, 
K2SO4,  and  KNO3. 

If  these  actions  are  to  be  classed  as  purely  physical,  we 

1  Graham  [Brit,  Ass.  Reports  for  1834.  579]  called  attention  to  the  difference 
between  strongly  heated  calcium  sulphate  and  the  same  substance  'in  a  state  for 
setting:'  but,  says  Graham,  "this  is  a  department  of  corpuscular  philosophy  which 
stands  much  in  want  of  further  development." 


CHAP.II.§  IOI]          MOLECULAR  COMPOUNDS.  2I/ 

should  not  expect  to  find  a  definite  limit  to  the  amount  of 
salt  or  acid  absorbed  by  each  hydrated  oxide :  but  van  Bem- 
melen's  researches  shew  that  the  process  tends  to  the  esta- 
blishment of  an  equilibrium  between  acid  (or  salt),  water,  and 
hydrated  oxide ;  that  this  condition  is  attained  slowly ;  and 
that  it  is  affected  by  the  relative  masses  of  the  reacting  sub- 
stances in  the  original  system.  Thus  less  acid  (or  salt)  is 
absorbed  from  a  very  dilute  than  from  a  more  concentrated 
solution,  but  the  amount  of  acid  or  salt  absorbed  increases 
much  more  slowly  than  the  increase  in  the  concentration  of 
the  solution  of  acid  or  salt.  The  final  equilibrium  is  not 
disturbed  by  the  addition  of  a  solution  of  acid  or  salt  of  the 
same  degree  of  concentration  as  that  surrounding  the  hy- 
drated dioxide,  but  if  the  added  solution  is  relatively  richer 
in  acid  or  salt  than  the  liquid  surrounding  the  dioxide,  then 
the  equilibrium  is  overthrown  and  the  absorption  of  acid  or 
salt  begins  again  and  proceeds  till  a  second  condition  of 
equilibrium  is  established. 

Some  hydrated  oxides  not  only  absorb,  but  also  par- 
tially decompose,  salts ;  for  instance,  when  the  hydrate 
2MnO2.5H2O  is  shaken  with  an  aqueous  solution  of  K2SO4, 
it  absorbs  a  definite  amount  of  the  latter  and  at  the  same 
time  separates  part  of  it  into  KOH  and  H2SO4.  Again,  one 
salt  is  sometimes  absorbed  in  preference  to  another;  thus  if 
MnO2.;rH2O  is  shaken  in  contact  with  H2SO4,  washed,  and 
again  shaken  in  contact  with  an  aqueous  solution  of  K2SO4, 
a  portion  of  the  H2SO4  which  had  been  absorbed  by  the 
hydrated  oxide  is  replaced  by  K2SO4 ;  again,  if  SiO2 .  4H2O 
is  allowed  to  absorb  A12C10,  is  then  washed  till  the  washings 
no  longer  contain  chlorine,  and  is  finally  shaken  with  an 
aqueous  solution  of  KC1,  it  is  found  that  some  of  the  KC1 
has  been  absorbed  and  some  of  the  AlaCl6  has  passed  into 
the  surrounding  liquid. 

These  substances  investigated  by  van  Bemmelen,  whether 
they  be  called  compounds  or  loose  combinations  of  salt  (or 
acid)  and  hydrated  oxide,  can  scarcely  be  regarded  as  com- 
posed of  molecules  each  built  up  of  atoms  of  metal,  oxygen, 
hydrogen,  and  the  elements  of  acid  or  salt,  but  rather  as 


2l8  ATOMIC   AND   MOLECULAR   SYSTEMS.          [BOOK  I. 

composed  of  molecular  groups  each  constituted  by  the  co- 
alescence of  molecules  of  acid  (or  salt),  water,  and  metallic 
oxide,  the  number  of  such  molecules  in  each  group  or  re- 
acting weight  being  variable  within  certain  limits.  The  pro- 
perties of  many  of  the  salts  of  the  weaker  acids — e.g.  car- 
bonic, boric,  and  sulphurous — are  regarded  by  van  Bemmelen 
as  explicable  in  terms  of  the  general  hypothesis  of  molecular 
compounds ;  he  would  regard  the  reacting  weights  of  these 
salts  as  molecular  groups,  more  stable  than  those  which  com- 
pose the  peculiar  class  of  bodies  just  described,  but  less  stable 
than  the  true  chemical  molecule. 

102  In  ms  second  paper  (loc.  cit.}  van  Bemmelen  has  more 
particularly  studied  hydrated  beryllium  oxide  BeO  .  ^'H2O. 
He  shews  that  two  varieties  of  this  oxide  exist,  viz.  a  gela- 
tinous and  a  granular  form  ;  that  the  former  alone  exhibits 
the  property  of  absorbing  acids  and  salts  from  aqueous  solu- 
tions ;  and  also  that  the  action  of  heat  on  the  two  hydrates  is 
different.  After  heating  to  220°  the  granular  hydrate  had 
lost  0*5  H2O,  and  was  now  much  altered  in  properties.  This 
fact — and  others  analogous  to  this  are  known — seems  to  shew 
that  by  the  application  of  energy  from  without  the  system  the 
parts  of  a  loose  molecular  group  may  be  caused  to  react  so 
as  to  bring  about  a  marked  change  in  the  properties  of  the 
body  composed  of  such  groups.  In  other  words,  the  com- 
parative readiness  with  which  definite  chemical  changes  may 
be  started  among  the  constituents  of  a  molecular  group 
appears  to  shew  that  although  these  constituents  are  held 
together  but  loosely,  nevertheless  they  are  not  merely  mixed. 
Thus,  As(CH3)2Cl  combines  with  C12  to  form  As(CH3)2Cl3; 
when  this  compound  is  heated  it  yields  As(CH3)Cl2+  CH3C1 ; 
then  As(CH3)Cl2  readily  takes  up  C12  to  form  As(CH3)Cl4, 
which  on  being  heated  separates  into  AsCl3  +  CH3Cl.  Now 
on  account  of  their  properties  some  of  these  compounds  must 
be  classed  as  molecular,  yet  under  the  influence  of  heat  the 
parts  of  the  molecular  groups  mutually  act  and  react  in  a 
way  analogous  to,  if  not  identical  with,  that  characteristic  of 
chemical  change.  But  such  phenomena  as  these  are  exactly 
what  might  be  expected  from  the  hypothesis  of  molecular 


CH.II.§§IO2,IO3]  ATOMIC  AND  MOLECULAR  COMPOUNDS.      219 

compounds ;  if  these  bodies  are  formed  of  groups  of  mole- 
cules we  should  expect  that  reactions  between  these  groups 
would,  in  many  cases,  easily  occur  and  result  in  the  produc- 
tion of  new,  less  complex,  groups,  or,  it  may  be,  new  mole- 
cules. That  a  substance  is  found  to  behave  in  a  definite 
manner  under  the  influence  of  this  or  that  reagent  cannot  be 
regarded  as  sufficient  evidence  for  classing  it  among  atomic 
rather  than  molecular  compounds.  Thus  the  observation  re- 
corded by  R.  W.  Atkinson1  regarding  the  identity  of  the  salts 
produced  by  mixing  (i)  SbCl3  and  3KBr,  and  (2)  SbBr3  and 
3KC1,  cannot  be  regarded  as  proving  that  the  product  of 
these  actions  is  built  up  of  molecules  represented  by  the  for- 
mula AfSbCl3Br3K3,  the  properties  of  which  are  conditioned 
only  by  the  mutual  interactions  of  the  atoms  Sb,  Cl,  Br,  and 
K.  Regarded  however  as  a  contribution  towards  solving  the 
questions  suggested  by  the  term  molecular  compounds,  the 
observations  made  by  Atkinson  are  of  interest,  as  shewing 
how  possible  it  is  to  obtain  substances  which  behave  in  some 
respects  as  molecular,  and  in  other  respects  as  atomic,  com- 
pounds. 

It  cannot  be  too  strongly  insisted  on  that  no  hypothesis 
has  been  proposed  regarding  molecular  compounds  which 
furnishes  us  with  a  definition  of  the  class  'molecular',  or  puts 
into  our  hands  an  instrument  for  determining  whether  a 
given  compound  belongs  to  this  class  or  to  the  class  of 
atomic  compounds.  What  the  hypothesis  does  is  to  negative 
the  notion  that  the  properties  of  all  compounds  are  to 
be  explained  by  the  conception  of  actions  and  reactions 
between  atoms  which  together  constitute  a  molecule,  and  to 
open  a  path  for  future  research  by  insisting  on  the  complexity 
of  chemical  phenomena,  and  the  folly  of  attempting  to  ex- 
plain all  in  terms  of  a  favourite  theory. 

103  But  the  consideration  of  molecular  compounds  leads  to 
the  discussion  of  questions  which  properly  belong  to  chemical 
kinetics  :  we  cannot  separate  these  bodies  from  their  environ- 
ment ;  they  are  members  of  a  system  which  is  continually 
undergoing  change  and  the  comparative  stability  of  which  is 

1  C.  S.  Jon  mat,  Trans,  for  1883.  289. 


22O  ATOMIC   AND   MOLECULAR   SYSTEMS.          [BOOK  I. 

the  result  of  never  ceasing  action  and  reaction  between  its 
parts.  Chemistry  is  not  a  collection  of  facts  regarding  the 
crystalline  forms,  melting  points,  boiling  points,  specific 
gravities,  &c.,  &c.,  of  elements  or  compounds ;  it  is  rather 
the  orderly  and  regulated  study  of  the  changes  which  these 
kinds  of  matter  undergo  and  which  result  in  more  or  less 
profound  modifications  in  the  properties  of  the  changing 
bodies. 

A  great  advance  has  certainly  been  made  by  replacing 
the  notion  of  a  molecule  as  an  undefined  quantity  of  matter 
constructed  of  groups  of  atoms  more  or  less  loosely  and 
vaguely  arranged,  by  that  conception  which  regards  the  mole- 
cule as  a  definite  and  definable  quantity  of  matter,  built  up 
of  atoms  arranged  in  an  orderly  manner,  and  exhibiting 
functions  dependent  on  the  nature,  arrangement,  and  mutual 
interactions,  of  these  atoms.  Among  the  functions  of  the  mole- 
cule we  must,  I  think,  place  the  power  of  combining,  under 
proper  conditions,  with  other  molecules  to  form  more  or  less 
complex  groups,  less  stable  than  the  molecules  of  a  gas,  and 
not  so  sharply  defined  from  other  groups  as  the  molecule  of 
one  compound  is  from  that  of  another.  Although  the  ex- 
planation of  the  properties  of  molecular  compounds  is  not 
to  be  brought  wholly  within  the  scope  of  the  hypothesis  of 
valency,  nevertheless  if  we  regard  the  formation  (or  non- 
formation),  and  the  relative  stabilities,  of  such  compounds, 
as  functions  of  all  the  molecules  concerned  in  their  synthesis, 
we  can  see  that  the  valencies  of  the  elementary  atoms  must 
be  important  factors  in  determining  the  production  of  mole- 
cular compounds1. 

Although  we  can  put  our  conception  of  the  molecule  into 
definite  terms,  yet  the  advance  of  knowledge  regarding  the 
properties  of  molecules  warns  us  against  attempting  to  define 
the  molecule  too  rigidly.  The  molecular  and  atomic  theory 

1  In  connexion  with  this  subject  compare  the  presidential  address  to  Section 
B  of  the  British  Association  at  Aberdeen  [1885].  In  this  address  Armstrong 
suggests  that  the  "formation  of  so-called  molecular  compounds  is  mainly  due 
to  peculiarities  inherent  more  especially  in  the  negative  elements — i.e.  the  non- 
metals  and  metalloids,  and  not  in  the  positive  elements — the  metals."  (See 
Nature,  32.  470.) 


CHAP.  II.  §  IO3]  ATOMIC  AND  MOLECULAR  COMPOUNDS.        221 

presents  the  chemist  with  the  conception  of  the  gaseous  mole- 
cule ;  by  applying  this  to  chemical  facts  he  arrives  at  the 
conception  of  the  atom,  a  conception  much  more  definite 
than  that  of  the  molecule ;  he  then  rebuilds  the  molecule  by 
putting  together  the  atoms  of  which  it  is  composed ;  but  he 
does  not  always  find  the  molecule  thus  re-constructed  to  be 
the  same  as  the  molecule  he  received  from  the  physicist. 
The  physical  definition  of  the  molecule  applies  in  strictness 
only  to  perfect  gases ;  but  the  chemist  has  to  deal  with  im- 
perfect gases,  and  also  with  liquids  and  solids. 

Notwithstanding  these  difficulties  fair  progress  has  been 
made  in  the  chemical  investigation  of  the  molecule.  We 
have  endeavoured  to  trace  this  progress,  as  it  appears  in  the 
methods  for  finding  the  relative  weights  of  atoms  and  mole- 
cules ;  in  the  distinction  between  the  properties  of  atoms  and 
the  properties  of  molecules  formed  by  the  union  of  atoms  ; 
in  the  chemical  conception  of  the  molecule  as  a  structure  of 
atoms  or  groups  of  atoms,  the  functions  of  which  structure 
are  dependent  on  the  nature,  number,  and  arrangement,  of  its 
parts;  in  the  development  of  this  conception  in  the  hypo- 
theses of  valency  and  isomerism  ;  and  in  the  recognition, 
forced  on  the  chemist  by  the  study  of  liquid  and  solid 
compounds,  that  although  the  properties  of  the  molecule  are 
conditioned  by  the  properties  of  its  parts,  it  has  also  an 
individual  existence  and  is  capable  of  interacting  as  a  whole 
with  other  molecules. 


[BOOK  i. 


CHAPTER  III. 

THE   PERIODIC   LAW. 

IN  the  preceding  Chapter  we  have  endeavoured  to 
trace  the  development  of  the  conceptions  of  the  atom  and 
the  molecule.  The  properties  of  compounds  are  regarded 
in  chemistry  as  the  properties  of  the  molecules  of  these  com- 
pounds, and  these  again  as  conditioned  by  the  properties 
of  the  atoms  which  compose  the  molecules.  Can  we  then 
trace  a  definite  connexion  between  the  properties  of  the 
•atoms  of  the  elements  and  the  properties  of  the  compounds 
formed  by  the  union  of  these  elements?  A  measurable  pro- 
perty of  the  atoms  is  their  relative  masses.  Is  there  any 
definite  and  definable  relation  between  the  atomic  weights 
and  the  properties  of  the  elements,  and  between  the  atomic 
weights  of  the  elements  and  the  properties  of  their  com- 
pounds ? 

104  Attempts  have  been  made  from  time  to  time  throughout 
the  preceding  50  or  60  years  to  trace  connexions  between 
the  atomic  weights  and  the  general  properties  of  groups  of 
elements. 

Soon  after  the  appearance  of  Dalton's  New  System  of 
Chemical  Philosophy,  an  hypothesis  was  promulgated  by 
Prout  to  the  effect  that  the  atomic  weights  of  the  elements 
are  whole  multiples  of  that  of  hydrogen  ;  but  the  researches 
of  Berzelius,  Marignac,  and  Stas,  shewed  that  this  hypothesis 
was  untenable.  A  modification  of  Prout's  hypothesis  was 
made  by  Dumas  which  appears  to  have  a  fair  probability  in 
its  favour. 


CH.III.§§I04,I05]  ARRANGEMENT  OF  THE  ELEMENTS.  223 

Gmelin,  Dumas,  Gladstone,  Cooke,  Kremers,  Pettenkofer, 
Odling,  and  especially  Newlands1,  who  was  among  the  earliest 
workers  in  this  field,  have  drawn  attention  to  points  of 
connexion  between  the  properties  and  the  atomic  weights  of 
elements.  In  1864  Newlands  arranged  a  number  of  elements 
in  order  of  their  atomic  weights,  and  shewed  that  these 
elements  were  divisible  into  groups  of  seven,  and  that  the 
properties  of  one  group  were  to  some  extent  repeated  in  the 
next  group.  "  The  eighth  element,"  said  Newlands,  "  starting 
from  a  given  element  is  a  kind  of  repetition  of  the  first,  like 
the  eighth  note  of  an  octave  in  music."  In  subsequent  papers 
Newlands  insisted  on  the  general  applicability  of  what  he 
called  the  '  law  of  octaves.' 

It  is  however  especially  to  Mendelejeff2  that  we  owe  the 
systematic  correlation  of  the  atomic  weights  with  the  chemical 
and  physical  properties  of  the  elements,  and  the  properties  of 
their  compounds. 

Lothar  Meyer8  has  also  made  important  contributions 
to  the  same  subject,  and  in  his  Modernen  Theorien  he  has 
gathered  together  the  more  important  facts  which  have  been 
established  concerning  the  relation  in  question. 
105  We  may  confidently  say  that  a  large  probability  has  been 
established  in  favour  of  the  hypothesis  that  the  properties 
of  the  elements,  and  of  the  compounds  of  each  element,  are 
periodic  functions  of  the  atomic  weights  of  the  elements. 
Lothar  Meyer  puts  the  general  statement  of  the  "Periodic 
Law"  in  this  form4:  "If  the  elements  are  arranged  in  order 
of  increasing  atomic  weights,  the  properties  of  these  elements 
I'ary  from  member  to  member  of  the  series,  but  return  more  or 
less  nearly  to  the  same  values  at  certain  fixed  points  in  tlie 
scries" 

Let  the  elements  be  arranged  in  the  order  of  their  atomic 
weights ;  let  this  list  of  elements  be  (broadly)  divided  into 

3  Chem.  News,1.  70;  and  10.  59,  94;  12.  83,  94;  13.  113,  &c.  Newlands' 
contributions  to  this  subject  have  been  gathered  together  and  published  in  a' 
small  volume  entitled  'On  the  Discovery  of  the  Periodic  Law'  [Spon,  1884]. 

2  Annalen,  Suppl.  Bd.  8.  133.     See  also  Chem.  News,  Vols.  40  and  41. 

3  Anna/en,  Suppl.  Bd.  5.  129,  and  7.  354  &c. 

4  Die  modernen  Theorien,  4th  Ed.  p.  136;  English  Ed.  p.  117. 


224  THE   PERIODIC   LAW.  [BOOK  I. 

series  of  sevens;  let  the  members  of  the  second  series  be 
placed  under  those  of  the  first,  those  of  the  third  under  those 
of  the  second,  and  so  on :  then  the  elements  contained  in  a 
vertical  column  are  said  to  form  a  group,  while  those  in  a 
horizontal  column  form  a  scries. 

In  this  arrangement  of  the  elements  each  group  cor- 
responds, for  the  most  part,  with  a  natural  family.  This  is 
more  clearly  shewn,  and  the  relations  between  the  atomic 
weights  and  the  properties  of  the  elements  are  more  distinctly 
developed,  if  certain  gaps  are  supposed  to  exist  in  the  list  of 
elements.  The  table1  on  p.  225  exhibits  the  arrangement  of 
the  elements  in  groups  and  series. 

106  Before  giving  a  detailed  explanation  of  this  table  let  us 
meanwhile   gather   together    some   of   the    best    established 
generalisations   concerning   the   periodic   connexion  of  pro- 
perties and  atomic  weights  of  the  elements. 

A  phenomenon  is  said  to  be  periodic  when,  if  the  con- 
ditioning circumstances  vary  continuously,  it  repeats  itself  at 
definite  intervals.  The  variable  under  consideration  is  the 
atomic  weight,  the  phenomenon  to  be  examined  is  the  nature 
of  each  chemical  element  and  its  compounds.  Although  it 
is  not  as  yet  possible  to  state  quantitatively  the  nature  of  the 
periodic  function  which  connects  the  atomic  weights  with 
the  general  properties  of  the  elements,  it  may  nevertheless  be 
established  that  the  function  in  question  is  periodic.  For 
this  purpose  it  will  be  necessary  to  break  up  the  phenomenon 
'nature  of  the  chemical  element  and  its  compounds'  and  to 
endeavour  to  shew  that  the  malleability,  ductility,  atomic 
volume,  power  of  forming  oxides  (or  chlorides)  of  definite 
composition,  position  in  electrical  series,  &c ,  of  the  elements 
do  vary  periodically  with  variations  in  the  atomic  weights  of 
these  elements2. 

107  Atomic  volume.     The  quotient  obtained  by  dividing  the 

1  Taken  from  a  paper  by  B.  Brauner  in  C.  S.  Journal  Trans,  for  1882.  78: 
atomic  weights  are  stated  in  round  numbers. 

2  For  greater  details  on  this  point  see  L.  Meyer,  Die  modernm    Thcoricn, 
4th  Ed.  pp.  139 — 173  (English  Ed.  pp.  117 — 150),  of  which  this  and  the  few 
following  pages  must  be  regarded  as  an  abstract. 


CHAP.  III.  §  lO/]   ARRANGEMENT  OF  THE  ELEMENTS.  225 


oo  en 
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II     II 


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bo  cj 


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M.  C. 


226  THE   PERIODIC   LAW.  [BOOK  I. 

atomic  weight  of  an  element  by  its  specific  gravity  in  the 
solid  form  is  called  the  atomic  volume  of  that  element.  This 
quotient  expresses  the  volume,  in  cubic  centimetres,  occupied 
by  an  amount  of  the  solid  element,  in  grams,  proportional  to 
the  atomic  weight  of  that  element. 

Arranging  the  elements  in  order  of  increasing  atomic 
weights  it  is  found  that  the  value  for  atomic  volume  reaches 
its  first  maximum  at  lithium,  that  it  then  diminishes  through 
beryllium,  boron,  &c.  and  again  increases  through  carbon,  &c. 
reaching  a  second  maximum  at  sodium  ;  the  other  maxima 
occur  at  potassium,  rubidium,  and  caesium. 

The  periodic  nature  of  the  connexion  between  atomic 
volumes  and  atomic  weights  becomes  very  apparent  when  the 
magnitudes  of  those  quantities  are  graphically  represented  as 
is  done  on  the  plate  facing  this  page1. 

The  maximum  points  on  the  curve  are  seen  to  be  occupied 
by  metals  of  low  specific  gravity,  while  the  minimum  points 
are  occupied  by  heavy  metals. 

The  position  of  an  element  on  the  curve,  with  reference  to 
the  preceding  and  succeeding  elements,  appears  to  be  inti- 
mately connected  with  the  properties  of  the  element  in  question. 
Thus  phosphorus  and  magnesium  on  the  one  hand,  and  calcium 
and  chlorine  on  the  other,  have  nearly  equal  atomic  volumes ; 
phosphorus  and  chlorine  are  followed  by  elements  the  atomic 
volumes  of  which  are  larger  than  their  own  (i.e.  are  situated 
on  ascending  portions  of  the  curve),  whereas  magnesium  and 
calcium  are  followed  by  elements  having  atomic  volumes 
smaller  than  their  own  (i.e.  are  situated  on  descending  portions 
of  the  curve). 

The  ductile  metals  are  placed  at  or  near  to  maximum  and 
minimum  points  on  the  curve ;  those  of  low  specific  gravity 
occurring  at,  and  immediately  after,  maximum  points,  and 
those  of  high  specific  gravity  at,  and  immediately  after, 
minimum  points.  The  brittle  heavy  metals  occur  in  sections 
4,  5,  and  7  immediately  before  the  minimum  points2. 

1  Only  those  elements  the  specific  gravities  of  which  in  the  solid  state  have 
been  directly  determined  are  included  in  the  curve ;  want  of  data  is  indicated  by  a 
broken  line. 

2  A  section  of  the  curve  means  the  part  situated  between  two  maxima;  section 


THE  PERIODIC    LAW. 


710      20      30     40      SO      60      70     80      90      100     III      120    130     WO     ISO      IM    170     ISO     190    200    210   220    230    240 

Thick  line  curve  shews  atomic  ntumes. 

Thin        ,  melting  Dointt 

Dotted  lints  indicate  that  data,  are   wanf/np 

'THIS     POINT      SHOULD  flf  PLACED   66  DIVISIONS  HICHfP 

IS— 2 


228  THE   PERIODIC   LAW.  [BOOK  I. 

The  elements  on  the  descending  parts  of  sections  2  and  3 
of  the  atomic  volume  curve  are  electropositive  and  form  basic 
hydroxides;  those  on  the  ascending  portions  of  the  same  sec- 
tions are  electronegative  and  form  acid  hydroxides.  Each  of 
sections  4  and  5  contains  four  groups  of  elements  arranged  in 
accordance  with  their  negative  or  positive  character.  Electro- 
positive elements  occur  on  the  first  portions  of  the  descending 
curve  in  each  of  these  sections  (K,  Ca ;  Rb,  Sr) ;  these  are 
followed  by  a  group  of  comparatively  negative  elements 
(V,  Cr,  Mn ;  Zr,  Nb,  Mo,  Rh,  Ru) ;  these  again  by  positive 
elements  (Fe,  Ni,  Co,  Cu,  Zn,  Ga  ;  Pd,  Ag,  Cd,  In) ;  and  after 
these  comes  a  group  of  negative  and  acid-forming  elements 
situated  on  the  ascending  part  of  the  curve  in  each  section 
(As,  Se,  Br;  [Sn],  Sb,  Te,  I).  Sections  6  and  7  are  too 
incomplete  to  allow  of  definite  conclusions  being  drawn 
regarding  the  positive  or  negative  character  of  the  elements 
situated  thereon. 

108  Fusibility.  The  melting  points  of  several  elements  have 
been  determined  by  various  observers1;  of  late  especially  by 
Carnelley2,  who  has  shewn  that  the  fusibility  of  the  elements 
varies  periodically  with  their  atomic  weights.  The  thin  line3 
curve  on  the  plate  on  p.  227  graphically  exhibits  this  con- 
nexion. 

A  connexion  may  be  traced  between  the  positions  of  an 
element  on  the  curve  of  atomic  volumes  and  on  that  of 

i  includes  hydrogen  only,  section  2  extends  from  lithium  to  sodium,  section  3 
from  sodium  to  potassium,  and  so  on.  There  are  probably  several  unknown 
elements  with  atomic  weights  greater  than  that  of  didymium  and  smaller  than 
that  of  tantalum  ;  the  curve,  if  complete,  would  probably  be  marked  by  a  sixth 
maximum  point  between  csesium  and  thorium,  this  part  of  the  curve  is  therefore 
said  to  comprise  two  sections  (6  and  7). 

1  See  Constants  of  Nature,  Part  I.  and  Supplement  to  do.     Also  L.  Meyer, 
loc.  cit.  pp.  145,  6.     (English  Ed.  pp.  129,  130.) 

2  Phil.  Mag.   [5]  8.  315  et  seq.:  this  paper  contains  a   good  resume  of  the 
periodic  law.     All  well  established  data  concerning  melting  points  are  collected 
in  Carnelley's  Tables  of  melting  and  boiling  points  (1885 — 87). 

3  The  values  of  the  melting  points  used  in  preparing  this  curve  are  taken  for 
the  most  part  from  Carnelley's  paper.     The  data  are  meagre,  hence  many  gaps 
occur  in  the  curve  (indicated  by  the  broken  lines) ;  many  of  the  numbers,  especially 
those  for  elements  at  and  near  to  maximum  points,  must  be  regarded  as  only 
rough  approximations  to  the  true  values. 


CH.  III.§§  108,  109]    EXPLANATION  OF  PERIODIC  LAW.  22Q 

fusibility ;  as  a  rule,  only  those  elements  which  are  situated 
on  ascending  portions  of  the  former  curve,  are  easily  fusible. 
Generalisations  have  also  been  made  concerning  the  con- 
nexions between  the  atomic  weights  of  groups  of  elements 
and  the  melting  points  of  these  elements  and  some  of  their 
analogous  compounds1.  Thus  the  melting  points  of  the 
haloid  salts  of  the  metals  in  Group  li.  (see  table  on  p.  225) 
are  considerably  higher  than  those  of  the  corresponding  salts 
of  the  metals  of  Group  III.: — 

e.g.  MgCl2     MgBr2;  CaCl2     CaBr2     CaI2;         SrCl2     SrBr2     SrI2; 

M.P.       708          695     ;  719         676         631  ;  825        630       507  ; 

but        A12C16      Al2Br6  A12I8. 

M.P.  very  low        90  185. 

Carnelley2  found  the  melting  point  of  beryllium  chloride 
to  lie  between  585  and  617°,  hence  he  concluded  that  beryl- 
lium belongs  to  Group  n.  and  that  the  formula  of  its  chloride 
is  BeCl2(Be  =  9'i),  and  not  BeCl8  or  Be2Cl6(Be=  I3'i5)3. 
The  data,  so  far  as  obtained,  concerning  the  boiling  points, 
crystalline  forms,  and  expansion  by  heat,  of  the  elements, 
indicate  that  the  connexion  between  these  constants  and  the 
atomic  weights  of  the  elements  is  of  a  periodic  character4. 

Hartley5  has  shewn  that  the  ultra-violet  spectra  of  elements  109 
of  the  same  group  shew  fairly  marked  analogies  as  regards 
general  character ;  the  spectra  hitherto  obtained  do  not  permit 
him  to  affirm,  or  deny,  the  existence  of  numerical  relations 
between  the  different  groups  of  lines,  sufficient  to  establish  a 
definite  periodic  connexion  between  the  atomic  weights  of  the 
elements  and  the  wave-lengths  of  the  lines  in  the  elementary 
spectra. 

That  there  exists  a  well-marked  connexion,  of  periodic 
character,  between  the  atomic  weights,  and  the  heats  of  com- 
bination of  the  elements  with  chlorine,  bromine,  and  iodine, 

See  Williams  and  Carnelley,  C.  S.  Journal  Trans,  for  1879.  563:  1880.  125. 

Proc.  R.  S.  29.  190.     See  also  Ibid.  Ber.  17.  1357. 

See  forward,  par.  in. 

For  details  see  L.  Meyer,  loc.  cit.  pp.  150—152.    (English  Ed.  pp.  130—152.) 

C.  £.  Journal  Trans,  for  1882.  84 :  permanent  photographs  of  the  ultra-violet 
spectra  of  various  elements  are  given  in  this  paper.  See  also  ibid.  Trans,  for  1883. 
390 :  and  Proc.  R.  S.  36.  462. 


230  THE   PERIODIC   LAW.  [BOOK  1. 

appears  to  have  been  first  pointed  out  by  Carnelley1.  A  little 
later  Laurie2  independently  drew  attention  to  this  subject  and 
exhibited  the  relation  in  question  by  means  of  a  curve. 
110  Having  thus  established  the  existence  of  a  connexion, 
distinctly  of  a  periodic  character,  between  the  atomic  weights 
and  the  general  nature  of  the  elements,  we  may  proceed  to 
consider  the  more  important  applications  of  the  periodic  law. 
This  consideration  will  also  serve  more  fully  to  elucidate  the 
meaning  of  the  law. 

The  law  has  been  applied  to  predict  the  properties  of 
unknown  elements.  In  the  nomenclature  of  unknown  ele- 
ments Mendelejeff  employs  as  prefixes  the  Sanskrit  numerals 
eka,  dui,  tri,  &c.  Thus  if  no  elements  were  known  with 
atomic  weights  equal  to  about  48  and  90,  two  gaps  would 
occur  in  Group  IV.  (see  table,  p.  225);  from  a  general  in- 
spection of  the  table  it  would  be  seen  that  these  gaps  ought  to 
be  filled  by  elements  bearing  a  more  or  less  close  analogy  to 
carbon ;  the  hypothetical  elements  would  be  called  eka-carbon 
and  dui-carbon  respectively.  At  the  time  of  MendelejefFs 
earliest  publication  there  was  no  element  known  which  could 
be  placed  opposite  the  atomic  weight  69  in  Group  ill.,  nor 
any  which  could  be  placed  opposite  the  atomic  weight  44  in 
the  same  group.  The  former  of  these  hypothetical  elements 
Mendelejeff  named  eka-aluminium,  the  latter  he  called  eka- 
boron.  The  properties  of  eka-aluminium  were  predicted  by 
Mendelejeff  from  considering  the  position  of  the  element  in 
the  same  group  as,  and  interposed  between,  aluminium  and 
indium,  and  in  the  same  series  as,  and  following  after,  zinc. 
In  1875  a  new  metal  was  discovered  by  L.  de  Boisbaudran. 
The  following  table  contains,  in  parallel  columns,  the  leading 
properties  of  this  metal,  and  those  enumerated  by  Mendelejeff 
as  characteristic  of  eka-aluminium :  the  hypothetical  metal 
of  Mendelejeff  and  the  gallium  of  de  Boisbaudran  are  one 
and  the  same  element. 

1  Proc.  R.  S.  29.  190. 

2  Phil.    Mag.   (5)   15.    42.       For  data  shewing  that  some  of  the  physical 
properties  of  compounds,  e.g.  melting  and  boiling  points,  vary  periodically  with 
variations  in  the  atomic  weights  of  the  constituent  elements,  see  Camelley,  Phil. 
Mag.  [5]  8.  368—70. 


CH.  III.§IIO]         PREDICTION    OF   ELEMENTS. 


231 


Eka-aluininium. 

Atomic  weight  about  69. 

Readily  obtained  by  reduction. 

Melting  point  low.     Sp.  gr.  =  5'9. 

Not  acted  on  by  air. 

Will  decompose  water  at  a  red  heat. 

Slowly  attacked  by  acids  or  alkalis. 

Will  form  a  potassium  alum  more 
soluble,  but  less  easily  crystallis- 
able,  than  the  corresponding 
aluminium  salt. 

Oxide  =  E12O3.     Chloride  =  E12C1<,. 


Gallium. 

Atomic  weight  =  69. 
Readily  obtained  by  electrolysing 
alkaline  solutions. 


Non-volatile,  and  but  superficially 
oxidised  in  air  at  bright  red  heat. 
Decomposes  water  at  high  temper- 
atures.    Soluble    in    hot    hydro- 
chloric   acid,    scarcely  attacked 
by  cold  nitric  acid  ;    soluble   in 
caustic  potash. 
Forms  a  well-defined  alum. 
I   Oxide  =  Ga2O3.    Chloride  =  Ga2Cl6. 

Eka-boron  belongs  to  Group  ill.  the  members  of  which 
group  combine  with  oxygen  to  produce  well-marked  oxides 
having  the  composition  R2O3.  In  its  properties  eka-boron 
ought  to  be  related  to  aluminium  as  calcium  is  to  mag- 
nesium, and  as  titanium  is  to  silicon.  The  atomic  weight  of 
eka-boron  must  be  about  43  —  46,  inasmuch  as  it  follows  K  (39) 
and  Ca  (40),  and  is  followed  by  Ti  (48)  and  V  (51).  Reason- 
ing from  these  data,  Mendelejeff1  predicted  certain  properties 
as  characteristic  of  eka-boron  and  its  salts.  Some  of  these 
are  placed  in  parallel  columns  with  a  description  of  the 
properties  of  the  metal  scandium*,  discovered  in  1879  by 
Nilson  :  — 


Eka-boron. 

Atomic  weight  about  44. 

Oxide  Eb2O3  soluble  in  acids ;  sp. 
gr.  about  3-5;  analogous  to  but 
more  basic  than  A12O3 ;  less  basic 
than  MgO  ;  insoluble  in  alkalis. 

Salts  of  Eb  colourless,  and  yield 
gelatinous  precipitates  with 
KOH,  K2CO3,  Na2HPO4,  &c. 

Sulphate,   Eb2.3SO4,  will   form  a 


double  salt  with  K2SO4,  probably 
not  isomorphous  with  the  alums. 
Chloride   EbCl3  or  Eb2Cl6,  sp.  gr. 
about  2,  less  volatile  than  Al2Clg. 
1  See  translation  of  MendelejefTs  paper  in  Chem.  News,  41.  pp.  71 — 72. 
8  Ber.  14.  1439.     See  also  Cleve,  Ber.  12.  2264:  and  Compt.  rend.  89.  419 
(abstract  of  latter  paper  in  C.  S.  Journal  for  1880.  8,  is  useful). 


Scandium. 

Atomic  weight  =  44. 

Oxide  Sc2O3  ;  sp.  gr.  =  3*8 ;  soluble 
in  strong  acids  ;  analogous  with 
but  more  decidedly  basic  than 
A12O3 ;  insoluble  in  alkalis. 

Solutions  of  Sc  salts,  colourless  and 
yield  gelatinous  precipitates  with 
KOH,  K2CO3,  and  Na2HPO4. 

Sulphate,  Sc2.3SO4,  forms  a  double 
salt,  not  an  alum, 

Sc23S04.3K2S04. 


232  THE    PERIODIC   LAW.  [BOOK  I. 

There  was  a  gap  in  Group  IV.  Series  5.  Eka-silicon  comes 
in  the  group  which  comprises  Si,  Sn,  and  Pb,  and  in  the 
series  including  Ga  and  As.  This  hypothetical  element  ought 
also  to  shew  analogies  with  other  elements  ;  thus, 

Es  :  Ti  : :  Zn  :  Ca  : :  As  :  V. 

From  the  position  of  eka-silicon^  Mendelejeff  concluded  that 
it  would  be  a  grey  metal,  obtained  by  reducing  the  oxide  by 
sodium,  fusible  with  difficulty;  it  would  decompose  steam 
very  slowly,  would  be  scarcely  acted  on  by  acids,  but  easily 
by  alkalis.  The  oxide,  EsO2,  (sp.  gr.  about  47)  would  be 
obtainable  by  burning  the  metal  in  air,  it  would  resemble 
TiO2,  but  would  be  less  basic  than  this  oxide,  although  more 
basic  than  SiO2;  the  hydroxide  would  be  soluble  in  acids, 
but  the  solution  would  be  easily  decomposed  yielding  an  in- 
soluble metahydroxide.  The  oxide  would  yield  a  series  of 
double  fluorides  M2EsF6  (M  =  alkali  metal)  isomorphous  with 
the  corresponding  salts  of  Si,  Ti,  Zn,  and  Sn.  The  fluoride 
EsF4  would  not  be  gaseous ;  the  chloride  EsCl4  would  be  a 
volatile  liquid  boiling  at  about  100°.  Eka-silicon  would  form 
volatile  organo-compounds. 

The  discovery  and  study  of  germanium,  by  Winkler2  have 
entirely  confirmed  Mendelejeff's  prediction :  eka-silicon  and 
germanium  are  one  and  the  same  element. 

Ill  The  periodic  law  has  also  been  successfully  used  as  a  guide 
in  the  comparative  study  of  the  properties  of  elements  already 
known. 

To  which  group  of  elements  does  beryllium  belong  ?  Is 
the  formula  of  the  oxide  BeO  or  Be2O3,  and  of  the  chloride 
BeCl2  or  BeCls?  Is  the  atomic  weight  of  beryllium  9  or  13-5  ? 

The  arrangement  of  the  elements  in  accordance  with  the 
periodic  law  seems  to  necessitate  the  placing  of  beryllium  in 
Group  II. ;  but  Nilson  and  Pettersson,  and  also  Humpidge,  who 
had  made  a  special  study  of  this  metal,  were  for  some  time 
strongly  of  opinion  that  beryllium  should  be  classed  with  the 

1  See  Chem.  News,  41.  83. 

2  Ber.  19.  210;  J.fiir  prakt.  Chemie  [a],  34.  177:  s.  also  Kriiss  and  Nilson, 
Ber.  20.  1296:  L.  de  Boisbaudran,  Compt.  rend.  102.   1291;  103.  452:  Kobb, 
Wied.  Ann.  29.  670:  also  L.  Meyer,  Ber.  20.  497. 


CH.III.§IIl]     CLASSIFICATION   OF  ELEMENTS.  233 

elements  which  form  oxides  of  the  composition  R8O8.  The 
atomic  weight  of  beryllium  =  # .  QT  :  the  data  regarding  the 
specific  heat  of  this  metal  have  been  presented  in  Chapter  I. 
par.  28,  and  it  has  there  been  shewn  that,  so  far  as  specific 
heat  data  are  concerned,  the  value  of  n  is  most  probably  I. 

Carnelley's  determination  of  the  melting-point  of  beryl- 
lium chloride  (see  ante,  par.  108)  points  to  the  beginning  of 
Group  II.  as  the  proper  position  for  beryllium,  and  hence  to 
the  number  9-1  as  the  atomic  weight  of  this  metal. 

The  general  chemical  characters  of  beryllium  salts  are 
summed  up  in  the  three  statements1  (Be  =  9'i); 

(1)  Li  :  Be=Be  :  B 

(2)  Li  :  Na  =  Be  :  Mg  =  B  :  Al 

(3)  Li  :  Mg  =  Be  :  Al  =B  :  Si. 

From  these  considerations  we  may  conclude  that  there  is  a 
large  probability  in  favour  of  the  value  9*1  for  the  atomic 
weight  of  beryllium.  This  conclusion  is  supported  by 
Hartley's  observations  on  the  spectrum  of  beryllium  and 
his  comparison  of  that  spectrum  with  those  of  metals  in 
Groups  II.  and  III.* 

Nilson  and  Pettersson3  have  succeeded  in  gasifying  beryl- 
lium chloride;  and  Humpidge4has  gasified  beryllium  chloride 
and  bromide.  The  determinations  of  the  vapour  densities  of 
these  compounds  shew  that  the  formulae  BeCl2  and  BeBrs 
(Be  =  9'i)  really  represent  their  molecular  weights. 

There  can  be  no  doubt  that  the  atomic  weight  of  beryllium 
is  9' i,  and  that  this  metal  is  to  be  placed  in  the  same  group 
as  magnesium,  calcium,  zinc,  strontium  &c.,  all  of  which  form 
oxides  having  the  composition  RO  and  chlorides  having  the 
composition  RC18. 

In  the  table  on  p.  225  tellurium  and  iodine  are  placed  in 
Series  7.  The  atomic  weight  of  iodine  was  for  many  years 
supposed  to  be  less  than  that  of  tellurium ;  nor  was  this 
result  contradicted  by  the  work  of  Wills8.  Nevertheless  the 

See  Brauner,  Ber.  14.  53. 

C.  S.  Journal  Trans,  for  1883.  316,  390:  also  Proc.  R.  S.  36.  461. 

Ber.  17.  987. 

Proc.  R.  S.  38.  188. 

C.  S.  Journal  Trans,  for  1879.  704. 


234  THE   PERIODIC  LAW.  [BOOK  I. 

analogies  between  sulphur,  selenion,  and  tellurium,  on  the 
one  hand,  and  chlorine,  bromine,  and  iodine,  on  the  other, 
are  so  marked  that  it  would  be  absurd  to  place  tellurium  in 
the  same  class  as  chlorine  and  bromine,  and  to  classify  iodine 
with  sulphur  and  selenion.  But  if  the  grouping  indicated 
by  the  periodic  law  is  to  be  adhered  to  the  atomic  weight  of 
tellurium  must  be  less  than  that  of  iodine.  Brauner1  in  1883 
made  an  experimental  criticism  of  the  method  by  which  the 
atomic  weight  of  tellurium  had  been  determined  by  Berzelius 
and  also  by  Wills  ;  he  shewed  that  this  method  almost  neces- 
sarily gives  results  which  are  too  high.  By  converting  tel- 
lurium into  the  very  stable  basic  sulphate  Te2O4SO3,  and  also 
by  syntheses  of  copper  telluride  Cu2Te,  Brauner  obtained  a 
series  of  values  for  the  atomic  weight  of  tellurium  varying 
from  124*94  to  I25'4  with  a  mean  value  of  125.  We  are  there- 
fore justified  in  placing  tellurium  in  Group  VI.  and  iodine  in 
Group  VII. 

Uranium  is  another  element  the  comparative  study  of  the 
properties  of  which  has  been  much  advanced  by  the  appli- 
cation of  the  periodic  law.  The  atomic  weight  of  this  element 
has  been  established  as  =  n.  120.  If  n  =  i,  the  three  oxides  of 
uranium  must  be  formulated  UO,  U2O8,  and  U3O4 ;  but  there 
is  no  place  for  an  element  with  this  atomic  weight  and 
forming  these  oxides  in  the  periodic  arrangement  If  how- 
ever n  =  2,  then  (U  =  240)  the  oxides  become  UO2,  UO3,  and 
U3O8,  and  uranium  finds  a  place  in  VI — 12.  The  preceding 
members  of  Group  VI.  which  belong  to  even  series,  viz.  Cr, 
Mo,  and  W,  yield  oxides  of  the  form  RO3  which  are  acid- 
forming.  But  a  comparative  study  of  the  relations  between 
the  properties  of  oxides  and  the  atomic  weights  of  the 
elements  in  these  oxides  shews,  that  as  the  atomic  weight 
of  the  elements  in  a  group  increases  the  acidic  character  of 
the  higher  oxides  formed  by  these  elements  becomes  less 
marked  (e.g.  CrO3  is  more  markedly  an  acidic  oxide  than 
MoO3  or  WO8).  Now  the  highest  oxide  of  uranium  is  an 
acid-forming  oxide,  but  its  acidic  functions  are  less  marked 
than  those  of  CrO3,  MoO3,  and  WO3;  salts  corresponding  to 

1  See  abstract  in  Ber.  16.  3055  (original  is  in  Russian). 


CH.  III.  §§III,  112]       LONG  AND  SHORT  PERIODS.  235 

K2CrO4  and  K2Cr2O7  in  which  Cr  is  replaced  by  U  are  known. 
Uranic  chloride,  UC14  if  11  =  240,  resembles  MoCl4  in  being 
volatile  and  decomposable  by  water. 

/.       atomic  weight\ 

The    atomic    volume      i.e.  -  of    the    four 

V         spec,  gravity  / 

metals,  Cr,  Mo,  W,  U,  increases  as  atomic  weight  increases, 
the  values  being  Cr  =  7'6;  Mo=  n  ;  W=  11  ;  U=  12*5. 

Hence  the  comparative  study  of  compounds  of  uranium, 
which  is  suggested  by  the  periodic  law,  justifies  the  adoption 
of  the  number  240  as  the  atomic  weight  of  this  metal. 

Determinations  of  the  densities  of  gaseous  uranium  bromide 
and  chloride,  and  of  the  specific  heat  of  pure  uranium,  have 
fully  confirmed  this  value.  (See  ante,  Chap.  I.  pars.  19  and  25  ; 
also  p.  59.) 

The  facts  enumerated  in  the  preceding  pages  undoubtedly  11 
establish  the  periodic  law  on  a  firm  basis,  and  justify  the  em- 
ployment of  this  law  as  one  of  the  main  guides  in  a  general 
scheme  of  chemical  classification1. 

The  following  arrangement  of  the  elements  (the  table  is 
taken,  with  a  few  alterations,  from  a  paper  by  Mendelejeff  in 
Ber.  13.  1804)  is  in  the  opinion  of  Mendelejeff  himself  the 
best  for  clearly  setting  forth  the  general  teaching  of  the 
periodic  law.  (See  next  page.) 

Each  group — except  Group  vill. — contains  members  be- 
longing to  odd  and  to  even  series ;  or  it  may  be  said  that 
each  vertical  column,  or  large  series,  is  subdivided  into  two 
parts  having  seven  elements  in  each.  The  entire  column, 
comprising  an  odd  and  an  even  series,  forms  a  '  long  period ' ; 
the  seven  members  in  the  even  or  in  the  odd  series  form 
a  'short  period.'  The  members  of  Group  vill.  form  'transition 
'periods'  from  series  4  to  5,  6  to  7,  (probably  8  to  9),  and 
10  to  u.  Including  the  'transition  periods,'  each  complete 
'  long  period  '  should  contain  17  elements. 

Because  of  its  peculiar  properties,  and  also  because  of  the 

1  The  system  of  classification  of  elements  and  compounds  adopted  in  Ele- 
mentary Chemistry  (Pattison  Muir  and  Slater)  is  based  entirely  on  the  periodic 
law. 

It  is  very  unfortunate  that  Mendelejeffs  Treatise  on  Chemistry  should  not 
have  been  translated  into  one  of  the  languages  of  Western  Europe. 


236  THE   PERIODIC   LAW.  [BOOK  I. 


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CH.  III.  §112]  ODD   AND   EVEN   SERIES.  237 

anomalous  relations  between  the  values  of  its  atomic  weight 
and  those  of  succeeding  elements,  hydrogen  is  regarded  as 
the  sole  representative  of  Series  I,  Group  I. 

Comparing  series,  we  find  closer  analogies  between  corre- 
sponding members  of  odd  or  of  even  series,  than  between 
those  of  odd  and  even  series :  thus,  comparing  Series  4  and  6, 
and  4  and  7,  potassium  and  rubidium  are  seen  to  be  more 
closely  related  than  potassium  and  silver;  calcium  and 
strontium,  than  calcium  and  cadmium ;  vanadium  and  nio- 
bium, than  vanadium  and  antimony.  Again,  comparing 
Series  5  and  7,  and  also  5  and  6,  it  is  seen  that  the  relations 
between  zinc  and  cadmium,  or  between  arsenic  and  antimony, 
are  closer  than  those  between  zinc  and  strontium,  or  arsenic 
and  niobium. 

Omitting  the  'typical'  elements  (see  p.  238)  it  may  be 
said  that,  as  a  rule,  the  most  markedly  nonmetallic  elements 
are  placed  in  odd  series.  Also,  that  the  passage  from  an 
even  to  an  odd  series  is  accompanied  by  a  gradual  change, 
but  that  from  an  odd  to  an  even  series  by  a  more  sudden 
change,  in  the  properties  of  the  elements ;  thus  chromium 
and  manganese  resemble  copper  and  zinc  much  more  than 
selenion  and  bromine  resemble  rubidium  and  strontium,  or 
than  tellurium  and  iodine  resemble  caesium  and  barium.  It 
may  also  be  laid  down  as  a  general  proposition  that  volatile 
organo-metallic  compounds  are  formed  only  by  metals  which 
occur  in  odd  series ;  should  such  compounds  be  hereafter 
formed  containing  metals  which  belong  to  even  series,  the 
properties  of  the  compounds  in  question  will  probably  differ 
much  from  those  of  the  volatile  organo-metallic  compounds 
at  present  known.  (Mendelejeff.) 

The  elements  which  form  the  'transition  periods'  (Group 
VIII.)  possess  many  characteristic  properties.  They  are  very 
infusible,  have  small  atomic  volumes,  and  occlude  oxygen  and 
other  gases  ;  oxides  of  the  form  RO4  are  met  with  in  this  group 
only ;  the  highest  oxides  are  basic  or  only  slightly  acidic ; 
these  metals  form  stable  alkaline  double  cyanides  K4RCy6. 
K3RCy6,  or  K2RCy4,  and  also  stable  ammoniacal  compounds1. 
1  See  Mendelejeff,  Chem,  News,  40.  267. 


238  THE   PERIODIC   LAW.  [BOOK  I. 

The  elements  in  Series  2  (from  lithium  to  fluorine),  and 
perhaps  the  first  member  of  Series  3,  viz.  sodium1,  are  grouped 
together  by  Mendelejeff  as  '  typical '  elements.  There  is  no 
'  transition  period '  coming  between  the  even  Series  2  and  the 
odd  Series  3  as  there  is  between  Series  4  and  5,  6  and  7,  and 
10  and  II.  The  mean  difference  between  the  atomic  weights 
of  two  elements  in  successive  even  series  and  in  the  same 
group  (e.g.  between  potassium  and  rubidium,  or  between 
rubidium  and  caesium)  is  45  ;  but  the  mean  difference  between 
the  atomic  weight  of  an  element  in  Series  4  and  the  corre- 
sponding element  (i.e.  the  element  in  the  same  group)  in 
Series  2  is  35  ;  hence  we  should  expect  to  find  the  relations 
of  Series  2  to  other  series  different  from  the  general  mutual 
relations  exhibited  by  these  other  series.  As  the  lower  mem- 
bers of  an  homologous  series  of  carbon  compounds  are  some- 
times characterised  by  the  possession  of  properties  which  do 
not  belong  to  the  higher  members,  so  the  elements  with 
atomic  weights  ranging  from  I  to  19  (?  23)  are  characterised 
by  special  properties  which  to  some  extent  mark  them  off 
from  the  other  elements. 

As  the  atomic  weight  increases  in  each  group,  the  basic 
character  of  the  higher  oxides  formed  by  the  members  of  the 
group  becomes  more  marked,  and  at  the  same  time  these 
oxides  become  more  easily  reduced.  It  is  also  to  be  noted 
that  the  composition  of  the  more  stable  haloid  and  oxyhaloid 
salts  (and  in  some  cases  of  the  more  stable  salts  as  a  whole) 
tends,  as  atomic  weight  increases,  to  correspond  in  form  with 
an  oxide  containing  less  oxygen  than  the  highest  oxide. 
These  statements  hold  good  more  especially  for  those 
members  of  a  group  which  occupy  the  odd  series.  Group  V. 
presents  a  good  example.  Sb2Og  is  more  basic  than  P2OS,  and 
Bi2O6  is  marked  by  an  almost  complete  absence  of  acidic  pro- 
perties. The  highest  oxides  of  this  group  belong  to  the  form 
RX5  (see  p.  240) ;  the  stable  haloid  and  oxyhaloid  salts  of 
phosphorus,  vanadium,  niobium  (PF5,  VOC13,  NbCl5),  belong 
to  the  same  form,  but  the  bismuth  haloid  and  oxyhaloid  salts 

1  Some  chemists  class  all  the  members  of  Series  i  and  3  (Li  to  Cl  inclusive) 
as  'typical'  elements, 


CH.  III.  §§112,113]  FORMS   OF   SALTS.  239 

are  BiCls,   BiBrs,  BiOCl,  BiOBr,  &c.,  which  belong  to  the 
form  RX3  corresponding  to  that  of  the  lower  oxide  Bi2O3. 

The  first  and  last  members  of  a  series,  and  more  especially 
of  a  '  long  period,'  present  marked  differences  in  their  general 
chemical  behaviour ;  thus  lithium,  potassium,  and  rubidium, 
the  first  members  of  the  long  periods  i,  2,  and  3,  are  strongly 
positive,  whereas  the  last  members  of  the  same  periods, 
viz.  chlorine,  bromine,  and  iodine,  are  typically  negative 
elements. 

Each  group  may  be  divided  into  two  sub-groups,  one 
comprising  the  elements  belonging  to  even  series,  the  other 
those  belonging  to  odd  series.  Calling  these  sub-groups 
families,  we  may  say  that  the  family-character  is  more 
marked  than  the  group-character  in  Groups  I.  and  VII.,  but 
that  in  Groups  III.,  IV.,  and  V.  the  group-character  prepon- 
derates, and  that  both  the  general  group-character  and  the 
special  family-character  are  well  seen  in  Groups  II.  and  VI. 

The  compositions  of  the  highest  oxides,  and  of  some  of  113 
the  other  salts,  appear  to  be  periodic  functions  of  the  atomic 
weights  of  the  elements.  In  dealing  with  this  question  it 
will  be  well  to  use  the  term  '  formula  weight '  rather  than 
molecular  weight,  as  the  molecular  weights  of  very  few  oxides 
have  been  determined. 

If  R  be  used  to  represent  the  mass  of  an  element  ex- 
pressed by  its  atomic  weight ;  and  if  X  represent  the  masses 
of  F,  Cl,  Br,  I,  expressed  by  the  respective  atomic  weights  of 
these  elements,  or  the  masses  of  the  groups  (OH),  (NO8), 
(C1O3),  &c.,  expressed  by  these  formulae,  or  the  masses  of 
the  elements  or  groups  of  elements  expressed  by  halves  of 
the  formulae,  O,  S,  (SOJ,  (CrOJ,  &c. ;  then  we  may  say  that 
the  oxides 

R20,  RO,  R203,  R02,  R20S, 
belong  respectively  to  the  forms 

RX,  RX2,  RXS,  RX4,  RX5: 
also  that  the  salts 

R9S04;  R.2NO3;  R-3NO8,  ROC1,  R2>3SO4,  RO.NOS;  ROC18, 
belong  respectively  to  the  forms 

RX;  RXt;  RX8,  RX8,  RX,,  RX8;  RX6. 


240  THE   PERIODIC   LAW.  [BOOK  I. 

In  this  way  it  becomes  possible  to  give  general  expressions 
for  the  forms  of  the  highest  stable  oxides  characteristic  of 
each  group  ;  thus, — 
Group     i  ii  in  iv  v  vi  vii  vin 

R20        R202      R203      R204       R205       R2O6      (R2O7)       (R2O8) 
or         RX         RX2       RX3        RX4        RX5        RX6        (RXr)        (RX8) 

This  statement  may  be  put  thus ;  the  number  of  oxygen 
atoms  in  the  general  expression  for  the  composition  of  the 
highest  stable  oxide  characteristic  of  each  member  of  a  series 
increases  as  the  atomic  weights  of  the  members  of  the  series 
increase. 

Most  of  the  stable  salts  (haloid  salts,  oxyhaloid  salts, 
nitrates,  sulphates,  chromates,  phosphates,  &c.)  characteristic 
of  the  members  of  each  group  belong  to  the  same  general 
form  (RX,  RX2,  &c.)  as  the  oxides.  But  in  every  group 
well-marked  salts  are  known  which  belong  to  higher  forms 
than  the  oxide  form :  thus,  some  of  the  members  of  Group  I. 
form  peroxides  (K2O2,  K2O4,  &c.) ;  some  of  the  elements  in 
Group  ii.  form  salts  (such  as  K2BeF4,  K2ZnCl4,  &c.)  of  the 
form  RX6;  salts,  such  as  BOC13,  KBF4,  KAlBr4,  &c.,  be- 
longing to  the  form  RX5,  are  found  in  Group  III.  The  forms 
of  the  highest  salts  belonging  to  each  group,  and  also  the 
oxide  forms,  are  given  by  Brauner1 ;  thus, — 

Group  i          ii  in  iv  v  vi       vn        vin 

Salt  forms  RXT  RX6  RX5  RX4  RX3  RX2      RX  /R2X  \ 

Oxide  forms  R2O  R2O2  R2O3  R2O4  R2O5  R2O6   (R2O7)  \RZOJ 
or  thus, — 

Salt  forms  RX7  RX6  RX5  RX4  RX3  RX2      RX  /R2X  \ 

Oxide  forms  RX  RX2  RX3  RX4  RX5  RX6   (RXr)  \RXj 

The  statements  generalised  in  these  expressions  can  be 
accepted  only  as  rough  approximations  to  general  truths. 
Oxides  of  the  forms  given  in  the  table  are  sometimes  less 
stable  than  oxides  of  other  forms;  e.g.  Cu2O  is  less  stable 
than  CuO,  PbO8  than  PbO,  &c. :  the  form  chosen  for  the 
highest  oxides  is  sometimes  represented  by  very  few  if  any 
actually  occurring  compounds ;  thus  the  form  R2O7,  charac- 
teristic of  Group  VII.,  finds  its  only  representative  in  I2O7, 

1  Sitzberichte  der  K.  Akad.  zu  Wien,  (math-naturwiss,  classe)  84.  116-;. 


CH.  III.  §§  H3,H4]  VALENCY.  24! 

and  the  existence  of  this  oxide  cannot  be  regarded  as  proved. 
Again,  salts  belonging  to  the  general  expressions  given  as 
representing  the  highest  forms  are  sometimes  fairly  character- 
istic of  the  group,  in  other  cases  it  is  only  by  a  dexterous 
manipulation  of  formulae  that  the  existence  of  such  salts  can 
be  discovered  ;  thus  a  great  many  well-marked  salts  of  the 
members  of  Group  V.  undoubtedly  belong  to  the  form  RX3, 
but  it  is  only  by  having  recourse  to  such  a  substance  as 
NaOH  .  3H2O  [Na(OH)(OH)3Hs]  that  a  salt  of  the  form  RX7 
can  be  found  belonging  to  Group  I. 

Relations  can  be  traced  between  the  general  forms  of 
hydrogen  and  hydroxyl  compounds,  especially  in  Groups  IV., 
v.,  vi.,  and  vu. ;  thus, — 


Group 
Hydrogen  compounds 

e.g. 

IV 

RH4 

SiH4 

V 

RH3 

PH3 

VI 

RH2 
SH2 

VII 

RH 
C1H 

Hydroxyl  compounds 
e.g. 

RH4O4 

Si(OH)4 

RH304 
PO(OH)3 

RH2O4 

S02(OH)2 

RHO4 

C1O,(OH) 

Dalton,  and  after  him  Berzelius,  sought  to  elucidate  the 
laws  of  atomic  synthesis ;  they  strove  to  find  forms  capable 
of  expressing  the  maximum  number  of  atoms  of  this  or  that 
element  which  could  combine  to  form  salts.  But  much  had 
to  be  done  before  these  limiting  forms  could  be  found  :  a  firm 
standing  ground  appears  to  be  now  gained  in  the  periodic 
law ;  to  build  a  structure  worthy  of  the  foundation  must  be 
the  work  of  the  future. 
14  The  valency  of  the  elementary  atoms  probably  varies 
periodically  with  the  relative  weights  of  these  atoms.  Thus 
taking  Series  2,  and  assuming  that  the  atom  of  lithium  is 
monovalent,  it  is  seen  that  in  this  series  the  valency  of  the 
elementary  atoms  increases  from  one  to  four,  and  again  di- 
minishes from  four  to  one : — 

Li          Be          B  C          N          O          F 

Valency        I  234321. 

If  the  evidence  were  sufficient  to  warrant  the  assumption 
that  the  valency  varies  in  every  series  in  the  same  way  as  in 
Series  2,  we  should  have  in  the  periodic  law  a  most  important 
aid  towards  determining  the  valencies  of  all  the  elementary 
M.C.  1 6 


242  THE   PERIODIC   LAW.  [BOOK  I. 

atoms.  But  the  evidence  at  present  available  concerning 
valency  does  not  permit  us  to  make  this  assumption.  A  pro- 
bable value  for  the  valency  of  an  elementary  atom  may  be 
deduced  from  the  position  of  the  element  in  the  periodic 
arrangement,  but  this  value  must  not  be  considered  as  final. 
It  has  indeed  been  sought  to  fix  the  valencies  of  elementary 
atoms  from  considerations  drawn  from  the  positions  of  these 
elements  in  the  periodic  classification ;  but  this  has  been 
done  only  by  attaching  to  the  term  'valency'  a  much  looser 
meaning  than  that  which  I  have  attempted  to  shew  must  be 
given  if  an  accurate  working  hypothesis  is  to  be  developed. 
In  applying  the  periodic  law  to  determine  the  valencies  of 
elementary  atoms,  the  formulae  of  oxides  and  of  solid  salts 
generally  have  been  employed  as  data  from  which  con- 
clusions might  be  drawn.  But  if  we  define  the  valency  of 
an  atom  as  the  maximum  number  of  other  atoms  with  which 
the  given  atom  can  directly  interact  in  any  molecule,  then,  to 
deduce  valencies  from  a  study  of  solid  salts,  we  must  assume, 
(i)  that  the  formula  of  a  solid  salt  certainly  represents  at 
least  the  proportion  between  the  numbers  of  atoms  of  each 
element  in  the  molecule  ;  (2)  that  the  atom,  the  valency  ot 
which  is  to  be  determined,  acts  on,  and  is  acted  on  by,  certain 
other  atoms  in  the  molecule — in  some  cases  it  may  be  action 
is  assumed  between  all  the  atoms,  in  other  cases  only  between 
some  of  the  atoms,  in  the  molecule ;  and  (3)  we  must  assume 
a  value  for  the  valency  of  each  atom,  other  than  the  given 
atom,  in  the  molecule.  Thus  to  take  an  extreme  case, 
hydrated  chloroplatinic  acid  H0PtCl6  .  6H..O  has  been  re- 
presented in  this  way 

VIII         III      IV 

H2Pt(-Cl  =  O  =  H2)fi; 

and  the  conclusion  has  been  drawn  that  the  platinum  atom 
is  octovalent. 

I  have  already1  discussed  assumptions  (2)  and  (3^1,  and 
have,  I  hope,  shewn  how  unsatisfactory  any  conception  of 
valency  must  be  which  in  the  present  state  of  knowledge  is 
based  on  the  study  of  other  than  gaseous  compounds.  A  solid 

1  See  chapter  n,  section  3,  par.  63. 


CH.  III.  §§  I  14,  I  1 5]  VALENCY.  243 

compound  is  prepared  with  definite  properties;  analysis  serves 
to  fix  the  composition  ;  the  atomic  weights  of  the  elements  in 
the  compound  being  known,  a  formula  is  found  : — but  to 
assume  that  this  formula  necessarily  represents  the  ratio 
between  the  numbers  of  different  elementary  atoms  in  the 
molecule  of  this  compound,  is  I  think  more  than  a  fair  in- 
ference from  the  facts.  For  is  not  this  to  assume  that  the 
'  chemical  unit '  of  the  solid  compound  is  a  molecule,  whereas 
it  may  very  probably  be  a  group  of  molecules  ?  The  defini- 
tion of  '  molecule '  is  a  physical  definition,  and  is  strictly 
applicable  only  to  gaseous  bodies.  The  properties  of  a  solid 
may  be  the  properties  of  a  number  of  little  definite  parts, 
each  of  which  decomposes  into  two  or  more  simpler  groups 
(molecules)  when  the  solid  is  gasified  ;  the  ratio  between  the 
numbers  of  atoms  in  the  true  molecules  may  be  different 
from  the  ratio  between  the  numbers  of  atoms  in  those  groups 
of  molecules,  which  form  the  building-stones  of  the  solid 
compound1. 

But  it  may  be  urged  that  a  much  wider  meaning  ought 
to  be  given  to  the  term  valency.  Better,  I  would  reply, 
employ  another  term  or  other  terms.  Let  us  make  as  much 
use  of  valency  as  we  can  ;  so  far  as  it  goes  it  is  definite,  with- 
out it  the  chemistry  of  carbon  compounds  especially  could 
not  have  made  the  advances  which  it  has  made.  But  it  is 
not  all. 

A  suggestion,  which  seems  fairly  probable,  has  been  made 
to  the  effect  that  the  maximum  valencies  of  the  atoms  increase 
from  the  members  of  Group  I.  to  those  of  Group  VII.,  but  that 
the  valency  actually  exhibited  in  the  majority  of  gaseous 
compounds  varies  from  a  minimum  in  Group  I.  to  a  maximum 
in  Group  IV.,  and  then  decreases  to  a  minimum  in  Group  VII. 
.15  In  applying  the  periodic  law  to  the  case  of  an  individual 
element,  it  is  necessary  in  the  first  place  to  consider  the 
properties  both  of  the  group  and  the  series  to  which  the 
element  belongs ;  then  the  position  of  the  element  in  the 
group  and  series  must  be  considered  ;  the  relations  of  other 

1  The  experiments  of  Hittorf  on  the  electrolysis  of  aqueous  solutions  of  cadmium 
iodide  are  very  suggestive  (see  ante,  p.  215). 

1 6— 2 


244  THE    PERIODIC   LAW.  [BOOK  I. 

elements,  situated  similarly  to  the  specified  element,  to  the 
other  members  of  their  groups  and  series  must  also  be  con- 
sidered, and  these  relations  must  be  compared  with  those  of 
the  special  element  under  consideration  ;  and  finally  the  re- 
lations of  group  to  group  and  of  series  to  series  in  the  entire 
scheme  must  be  looked  to.  The  method  is  strictly  com- 
parative. It  is  necessary  to  study  classes  of  elements  and 
compounds,  and  to  compare  class  with  class  and  individual 
with  individual,  before  just  conclusions  can  be  drawn1. 

The  periodic  law  emphasises  the  existence  of  typical  forms 
for  the  compounds  of  elements ;  it  points  to  limiting  values 
for  the  numbers  of  atoms  which  can  be  associated  together 
in  groups.  It  teaches  the  importance,  in  the  chemistry  of 
solid  and  liquid  compounds,  of  the  law  of  multiple  proportions. 
It  reminds  us  that  at  present  we  must  study  the  properties  of 
groups  of  compounds,  that  we  must  sum  up  these  properties 
in  the  simplest  possible  formulae,  and  that  the  whole  chemical 
history  of  each  compound  must  determine  the  form  to  be 
given  to  the  symbol  by  which  we  express  that  history.  It 
tells  us  that  although  we  do  not  know  whether  such  formulae 
do  or  do  not  represent  the  relative  weights  of  the  molecules 
of  the  bodies  formulated,  nevertheless  these  formulae  can  be 
classified  under  a  few  types ;  and  that  thus  a  certain  amount 
of  order  can  be  introduced  into  the  classification  of  solid  and 
liquid  compounds,  general  conclusions  can  be  drawn,  and  pre- 
dictions can  be  made  which  may  be  submitted  to  the  test  of 
experiment.  And  while  doing  this,  the  periodic  law  keeps 
before  us  the  necessity  of  from  time  to  time  modifying  our 
scheme  of  classification  ;  it  reminds  us  that  a  typical  classifi- 
cation is  of  necessity  temporary,  but  that  just  by  reason  of  its 
elasticity  it  is  suited  to  the  present  needs  of  the  chemistry  of 
solid  and  liquid  substances2. 

1  The  student  should  work  out  some  cases  in  detail ;  say  lead  in  Group  iv., 
antimony  in  Group  v.,  and  cadmium  in  Group  n. 

2  It  is  interesting  to  observe  in  the  applications  of  the  periodic  law  the  survival, 
in  modified  and  more  precise  form,  of  the  old  conception  of  the  element  as  an 
essence  or  principle,  capable  of  impressing  on  all  substances  into  which  it  entered 
properties  sufficiently  definite  to  mark  off  these  substances  from  all  others  which 
did  not  contain  this  principle. 


CHAP.  III.  §  115]  SUMMARY.  245 

An  interesting  paper  on  the  periodic  law,  especially  as  applied  to  the  clas- 
sification cf  elements  and  compounds,  by  T.  Bayley,  will  be  found  in  Phil. 
Mag.  (5)  13.  26.  Other  important  papers  on  the  same  subject,  by  Carnelley, 
are  published  in  Phil.  Mag.  (5).  18.  i  et  seq.\  do.  do.  (5).  20.  259.  In  these 
papers  the  periodic  law  is  illustrated  by  considering  the  melting  and  boiling 
points,  and  to  some  extent  also  the  heats  of  formation,  of  the  halogen  compounds 
of  the  elements,  and  also  the  compounds  of  elements  with  organic  radicles,  and 
also  the  occurrence  in  nature  of  the  elements,  and  the  relations  between  the 
colours  of  compounds  and  the  atomic  weights  of  their  constituent  elements;  and 
the  facts  thus  obtained  are  applied  to  determine  the  values  to  be  assigned  to  the 
atomic  weights  of  various  elements,  and  also  the  positions  of  these  elements  in 
the  general  scheme  of  classification  based  on  the  law  in  question. 


[BOOK  i. 


CHAPTER  IV. 

APPLICATIONS    OF    PHYSICAL    METHODS    TO    QUESTIONS    OF 
CHEMICAL    STATICS. 

116  CHEMISTRY  being  a  more  concrete  science  than  physics 
must  of  necessity  derive  help  in  solving  its  problems  from 
the  use  of  physical  methods  of  investigation ;  but  while 
using  such  methods  the  chemist  ought  not  to  forget  that  his 
aim  is  to  find  answers  to  chemical,  not  to  physical,  questions. 

Minute  descriptions  of  physical  processes  and  details  of 
physical  experiments  are  not  demanded  in  a  treatise  on 
physical  chemistry;  much  less  is  there  required  elaborate 
enunciations  of  the  methods  of  calculation  employed  in 
physical  researches.  Such  things  give,  it  is  true,  an  appear- 
ance of  great  accuracy  and  profound  knowledge  ;  but  the  ap- 
parently accurate  knowledge  and  full  discussion  of  physical 
details  too  frequently  serves  as  an  excuse  for  loose  state- 
ments and  superficial  generalisations  regarding  those  vital 
chemical  questions  for  answering  which  so  vast  a  collection  of 
'precautionary  and  vehiculatory  gear'  has  been  provided.  In 
attempting  to  give  an  outline  of  the  more  important  appli- 
cations of  physical  methods  to  chemistry  one  is  also  liable 
to  err  in  the  other  direction  :  vague  statements  to  the  effect 
that  the  boiling  points  of  homologous  hydrocarbons  exhibit 
constant  differences,  or  that  the  chemical  constitution  of 
carbon  compounds  is  intimately  connected  with  their  optical 
activity,  or  that  chemical  actions  which  involve  a  degradation 
of  energy  in  the  reacting  systems  frequently  occur, — state- 
ments such  as  these  are  utterly  inadequate. 


CH.  IV.  §§  1 1 6,  1 1/]  APPLICATIONS  OF  PHYSICAL  METHODS.  247 

I  cannot  hope  to  avoid  both  dangers :  but  I  may  venture 
to  believe  that  the  contents  of  the  present  chapter  will  be 
of  some  assistance  to  those  who  attempt  to  gain  clear  con- 
ceptions of  some  of  the  important  phenomena  forming  the 
subject-matter  of  physical  chemistry. 

Some  of  the  physical  methods  employed  by  the  chemist 
as  aids  in  attempts  to  solve  the  questions  of  chemical  statics 
have  been  considered  in  the  foregoing  chapters  of  this  book ; 
in  addition  to  these  I  shall  consider  the  following;  (i)  ther- 
mal methods,  (2)  optical  methods,  (3)  methods  which  in- 
volve measurements  of  the  volumes  of  reacting  substances, 
(4)  methods  based  on  determinations  of  'etherification-values', 
and  (5)  a  few  miscellaneous  methods. 


SECTION    I.     T formal  Methods*. 

117  The  principle  of  the  conservation  of  energy  lies  at  the 
root  of  all  thermo-chemical  investigation.  When  two  or 
more  chemical  substances  react  so  as  to  produce  a  new 
system,  or  new  systems,  of  substances,  mechanical  work  may 
be  done  by  expansion,  electrical  currents  may  be  produced, 
heat  may  be  generated,  and  energy  may  be  lost  to  the 
system  in  the  forms  of  sound  or  radiant  heat.  The  sum  of 
these  various  kinds  of  energy,  together  with  the  energy  re- 
maining in  the  final  system,  must  be  equal  to  the  energy 
which  was  present  in  the  original  system.  A  very  large  part 
of  the  energy  set  free  during  chemical  changes  generally 
leaves  the  changing  systems  in  the  form  of  heat;  hence, 
measurements  of  the  quantities  of  heat  produced  during 
definite  chemical  processes  afford  valuable  information  with 

1  The  principal  text-books  on  the  subject  are  NAUMANN'S  Lehr-  und  Hand- 
bitch  tier  Thermochemie  (1882).  THOMSEN'S  l^hermochemische  Untersuchungen, 
containing  in  a  systematic  form  the  work  of  many  years  which  has  hitherto  been 
scattered  through  various  memoirs,  4  vols.  (1882-86).  BERTHELOT'S  Essai  de 
Mi'caniqne  Chimiqite  fondcc  snr  la  Thennochiinit:,  i  vols.  (1879)  with  supple- 
ment. JAHN'S  Die  Grundsdtze  der  Thermochemie  (1882).  PATTISON  MUIR'S 
The  Elements  of  Thermal  Chemistry  (1885). 

The  first  book  of  the  second  volume  of  OSTWALD'S  Lehrbuch  der  Allgentfiiun 
Choiric  is  devoted  to  thermal  chemistry  (1887). 


248  THERMAL   METHODS.  [BOOK  I. 

respect  to  the  differences  between  the  amounts  of  energy 
possessed  by  the  systems  in  their  original  and  final  states. 
To  measure  such  differences  of  energy  is  the  primary  aim  of 
thermal  chemistry. 

We  are  accustomed  to  conceive  of  most  chemical  changes 
as  divisible  broadly  into  two  parts,  (i)  separation  of  molecules 
into  atoms,  (2)  re-arrangement  of  atoms  to  form  new  mole- 
cules. We  picture  to  ourselves  the  final  arrangement  of  the 
atoms  as  'dependent  on  the  nature  of  these  atoms,  and  on 
their  relative  positions  in  the  molecules  which  composed  the 
original  system,  that  is  to  say,  we  picture  the  progress  of 
mutual  actions  and  reactions  among  the  separated  atoms. 
We  know  little,  or  nothing,  of  the  causes  of  this  re-arrange- 
ment ;  but  we  are  accustomed  to  say  that  the  atoms  interact 
because  of  their  mutual  affinities. 

A  consideration  of  the  circumstances  under  which  chemical 
changes  proceed  and  of  the  connexions  between  these  and  the 
thermal  changes  which  accompany  them  will,  I  think,  make 
it  evident  that  measurements  of  the  quantities  of  heat  pro- 
duced during  chemical  occurrences  do  not  represent  measure- 
ments of  the  'chemical  affinities  !1  of  the  reacting  atoms  ;  but 
these  measurements  do  enable  us  to  draw  conclusions  as  to 
the  constitution  of  chemical  substances,  and  the  general  laws 
of  chemical  change. 

The  bearing  of  thermochemical  measurements  on  the 
subjects  of  affinity  and  chemical  equilibrium  in  general  will  be 
considered  in  the  second  book :  in  the  present  section  I  pro- 
pose to  give  a  very  brief  sketch  of  the  methods  of  thermal 
chemistry,  and  an  outline  of  the  more  important  results  ob- 
tained relating  to  allotropy,  isomerism,  nascent  state,  and 
other  phenomena  of  chemical  statics,  referring  the  student 
for  more  detailed  information  and  discussion  to  my  Elements 
of  Thermal  Chemistry. 

118  The  notation  of  thermal  chemistry  used  by  Thomsen  is 
very  simple:  the  formulae  of  the  reacting  substances  are 
enclosed  in  a  square  bracket,  and  each  formula  is  separated 
from  the  other  by  a  comma.  The  formulae  are  always  taken 

1  See  post,  Book  n. 


CHAP.  IV.  §  1 1 8]    NOTATION  OF  THERMAL  CHEMISTRY.          249 

to  represent  so  many  grams  of  the  substances.  The  unit  of 
heat  adopted  is  that  quantity  which  raises  the  temperature  of 
i  gram  of  water  at  about  18°  C.  through  i°  C.  The  signs 
+  and  —  are  used  to  express  quantities  of  heat  produced  or 
which  disappear.  Thomsen  writes  the  figure  expressing  the 
number  of  atoms  of  each  element  above  the  symbol  of  that 
element1. 

Thus,  the  formula  [H2,  Cl2]  =44,000  +  ,  means  that  a 
quantity  of  heat,  sufficient  to  raise  the  temperature  of  4/1,000 
grams  of  water  at  about  18°  through  i°,  is  produced  during 
the  chemical  process  represented  in  ordinary  notation  by 
H2+C12=2HC1,  the  quantities  of  hydrogen  and  chlorine 
being  taken  in  grams.  The  symbol  Aq,  separated  by  a 
comma  from  another  symbol,  means  that  a  large  excess  of 
water  is  present  and  that  its  effect  in  the  total  thermal 
change  is  taken  into  account;  thus,  [HC1,  Aq]  =  17,320  +  , 
means  that  17,320  gram-units  of  heat  are  produced  during 
the  solution  of  36*5  grams  of  hydrochloric  acid  in  a  quantity 
of  water  so  large  that  addition  of  more  water  would  not  affect 
the  thermal  value  of  the  reaction.  [H2,  Cl2,  Aq]  =  61,320+, 
means  that  the  combination  of  2  grams  of  hydrogen  with  71 
grams  of  chlorine  in  the  presence  of  an  unlimited  amount 
of  water  is  attended  with  the  production  of  61,320  gram-units 
of  heat.  [HClAq,  KOHAq]=  13,750  +  ,  means  that  when 
36*5  grams  of  HC1  dissolved  in  a  large  excess  of  water  react 
with  56  grams  of  KOH,  also  dissolved  in  a  large  excess  of 
water,  13,750  gram-units  of  heat  are  produced. 

The  symbol  H2O  is  used  as  in  ordinary  notation  to  repre- 
sent 1 8  grams  of  water  ;  thus 

(1)  [Mn,  O2,  SO2,  4H2O]  =  190,810+; 

(2)  [MnSO44H2O,  Aq]=      1770+; 

mean,  (i)  that  in  the  formation  of  the  amount,  in  grams, 
of  crystallised  manganous  sulphate  expressed  by  the  formula 
MnSO44H2O,  from  the  amounts,  in  grams,  of  manganese, 

1  Thomsen  appears  to  be  the  only  chemist  who  systematically  writes  the  indices 
above  the  symbols  of  elements  in  the  formulas  of  thermal  chemistry.  Thomsen 
also  sometimes  uses  the  colon  in  place  of  the  comma  to  express  chemical  reaction 
between  the  substances  whose  formulae  are  separated  by  this  symbol. 


250  THERMAL   METHODS.  [BOOK  I. 

oxygen,  sulphur  dioxide,  and  water,  expressed  by  the  respec- 
tive formulae  Mn,  O2,  SO2,  and  4H2O,  190,810  gram-units 
of  heat  are  produced:  (2)  that  1770  gram-units  of  heat  are 
produced  in  the  solution  of  the  foregoing  number  of  grams  of 
crystallised  manganous  sulphate  in  an  unlimited  quantity 
of  water. 

Generally  then1,  let  r=the  thermal  value  of  a  chemical 
change :  let  the  change  be  the  formation  of  a  definite  amount 
of  a  compound2  viz.  (XaY6Zc),  consisting  of  a  parts  by 
weight  of  the  element  X,  b  parts  by  weight  of  the  element  Y, 
and  c  parts  by  weight  of  the  element  Z;  then 

r=[X",  Y",  Z'-}  (i). 

Let  the  compound  Xa  YbZc  be  produced  as  before,  but  in 
presence  of  a  large  excess  of  water  which  holds  it  in  solution ; 

then 

r=[X*,   Y",  Z<,  Aq]  (2). 

Let  the  substance  Xa  YbZc  already  existing  be  dissolved  in 
an  unlimited  amount  of  water;  then 

r=[*-I"Z<,  Aq]  (3). 

Let  the  compound  XYbe  decomposed  by  the  element  Z 
with  formation  of  XZ  and  Y ;  we  get  the  expression 

r=[XY,Z]  =  [X,Z]-[X,  Y]  (4), 

that  is,  the  total  thermal  change  consists  of  two  parts,  (a) 
the  heat  used  in  separating  XY  into  X  +  Y,  and  (b)  the  heat 
produced  in  the  union  of  X  and  Z  to  form  XZ. 

Finally  let  the  compound  XY  react  with  the  compound 
VZ  to  produce  XZ  and  VY;  the  value  of  r  is  found  by 

the  formula 

r=[X,Z}  +  [V,    Y]-[X,  Y]-[V,Z] (5). 

Equations  (i)  to  (3)  have  already  been  illustrated.  As  an 
example  of  the  use  of  (4)  we  may  take  the  reaction  of  zinc 
with  hydrochloric  acid  whereby  zinc  chloride  and  hydrogen 
are  produced  ; 

[Zn,  2HClAq]  =  [Zn,  CPAq]-2[H,  ClAq]; 

1  Thomsen,  Thermochemische  Untersuc/iungen,  1.  5  et  seq. 

2  In  many  cases  we  may  use  the  term  '  molecule '  in  place  of  '  definite  amount ', 
and  'atom'  in  place  of  'parts  by  weight':  but  as  we  shall  frequently  deal  with 
solids  and  liquids  it  is  better  at  present  not  to  speak  of  atoms  and  molecules. 


CH.  IV.  §  I  1 8]         NOTATION  OF  THERMAL  CHEMISTRY.  25  I 

or  that  of  iron  with  a  solution  of  copper  sulphate  to  produce 
ferrous  sulphate  and  copper  ; 

[CuSO4Aq,  Fe]  =  [Fe,  SO4Aq]-[Cu,  SO4Aq]. 

As  an  illustration  of  (5)  the  decomposition  of  PbO  by  H2S 
resulting  in  the  production  of  PbS  and  H2O,  may  be  used  ; 
[PbO,  H^S]  =  [Pb,  S]  +  [H2,  O]-[Pb,  O]-[H2,  S]. 

Ostwald  (Lehrbuch)  uses  a  system  of  notation  which 
expresses  more  facts  about  each  reaction  than  that  em- 
ployed by  Thomsen.  The  latter  does  not  indicate  the  pro- 
ducts of  the  chemical  change  the  thermal  value  of  which 
is  stated.  Ostwald  employs  the  ordinary  notation,  but  sup- 
plements each  equation  by  a  statement  of  the  quantity  of 
heat  which  is  produced  or  disappears  in  the  reaction :  he  also 
uses  three  kinds  of  type  to  express  the  state  of  aggregation 
of  the  various  bodies.  A  symbol  printed  in  thick  type 
indicates  a  solid,  ordinary  type  indicates  a  liquid,  and  italics 
shew  a  gas.  The  following  examples  illustrate  Ostwald's 
system. 

(1)  H 2 +Cl.i=2JfCl+  44,000. 

(2)  2fftS+  2l2=4//7+  28  -  34,000. 

(3)  2H2SAq  +  2l2Aq  =  4HIAq  +  2S  +  34,ooo. 

These  equations  tell  (i)  that  the  sum  of  the  internal 
energies  of  2  grams  of  gaseous  hydrogen  and  71  grams  of 
gaseous  chlorine  exceeds  the  internal  energy  of  73  grams 
of  gaseous  hydrochloric  acid  by  a  quantity  equal  to  44,000 
gram-units  of  heat,  and  (2)  and  (3)  that  the  sum  of  the 
internal  energies  of  68  grams  of  gaseous  sulphuretted 
hydrogen  and  508  grams  of  solid  iodine  is  equal  to  that 
of  512  grams  of  gaseous  hydriodic  acid  and  64  grams  of 
solid  sulphur  diminished  by  34,400  gram-units  of  heat,  but 
that  the  sum  of  the  energies  of  the  same  masses  of  hydrogen 
sulphide  and  iodine  in  dilute  aqueous  solution  exceeds  the 
sum  of  the  energies  of  the  same  mass  as  before  of  hydriodic 
acid  in  dilute  aqueous  solution  and  the  same  mass  as  before 
of  solid  sulphur  by  34,400  gram-units  of  heat.  If  it  is 
required  to  indicate  a  particular  temperature  at  which  one 
or  other  of  the  reacting  bodies  is  caused  to  take  part  in 


2$2  THERMAL   METHODS.  [BOOK  I. 

the  reaction,  this  is  done  by  Ostwald  by  putting  the  number 
indicating  the  temperature  in  small  figures  in  a  bracket  below 
the  symbol  of  the  body;  thus  S(2o)means  32  grams  of  solid  sulphur 
at  20°;  2S(m)  means  64  grams  of  gaseous  sulphur  at  600°.  The 
value  of  the  thermal  change  accompanying  a  change  of  state,  or 
a  change  of  the  same  body  from  one  temperature  to  another, 
may  be  very  easily  indicated  by  using  Ostwald's  system  of 
notation.  Thus  H2O(0)  =  H20«»  +  1440,  or  wnat  is  tne  same 
thing  H2O(0)  —  H20(o)  =  144°>  tells  that  the  change  from 
1  8  grams  of  liquid  water  at  o°  to  the  same  mass  of  solid 
water  at  the  same  temperature  is  accompanied  by  the  pro- 
duction of  1440  gram-units  of  heat.  Again  Cuaoo)  =  Cu(U)  +  600 
tells  that  6y5  grams  of  solid  copper  at  100°  contain  energy 
equal  to  600  gram-units  of  heat  more  than  63-5  grams  of 
solid  copper  at  o°. 

Both  Thomsen's  and  Ostwald's  system  of  notation  will 
be  used  in  this  book  ;  the  latter  especially  when  it  is  desired 
to  indicate,  shortly  and  clearly,  differences  in  the  states  of 
aggregation  of  the  reacting  bodies. 

119  A  distinction  has  been  drawn  between  so-called  exothermic 
and  endothennic  changes  ;  the  former  are  accompanied  by 
production,  the  latter  by  disappearance,  of  heat. 

Let  (PaQb]  represent  the  energy  in  a  compound  formed  of 
a  parts  of  element  P  and  b  parts  of  element  Q:  let  (/**)  and 
(<2*)  represent  the  energy  in  a  parts  of  P,  and  in  b  parts  of 
Q,  respectively;  then,  inasmuch  as  the  energy  in  any  system 
resulting  from  a  definite  chemical  change  is  equal  to  the 
difference  between  the  energy  in  the  original  system  from 
which  it  was  produced  and  that  lost  to  the  system  during  the 
process,  it  follows  that 


assuming  that  the  heat  produced  in  the  formation  of  PaQ" 
measures  the  total  loss  of  energy  ; 

and  therefore  (P")  +  (Q*)  >  (/>«£*). 

This  equation  represents  an  exothermic  change. 

But  in  some  cases  a  chemical  change  occurs  only  when  heat 
is  added  to  the  changing  system  from  without  ;  in  such  a  case 


CHAP.  IV.  §  IIQ]     EXOTHERMIC   AND   ENDOTHERMIC.  253 


and  therefore  (Pa]  +  (Q*)  <  (P"Q?}- 

This  equation  represents  an  endothermic  change. 

In  some  cases,  a  chemical  reaction  which  seems  to  be 
accompanied  by  disappearance  of  heat  is  found,  on  more 
careful  study,  to  form  one  member  of  a  series  of  changes  the 
thermal  sum  of  which  is  represented  by  a  positive  quantity. 
Indeed  any  chemical  reaction  is  a  most  complex  phenome- 
non when  regarded  from  the  thermal  point  of  view;  physical 
changes  (expansion  or  contraction,  passage  from  solid  to 
liquid  or  gas,  or  vice  versa,  &c.,  &c.)  form  part  of  the  total 
change  the  thermal  value  of  which  is  set  down  in  a  lump 
sum.  The  purely  chemical  part  of  the  change  may  be  ac- 
companied by  disappearance  of  heat,  while  the  complete 
occurrence  may  involve  the  production  of  heat. 

The  following  example  will  serve  to  illustrate  the  use  of 
the  terms  endothermic  and  exothermic. 

Naumann  l  shewed  that  no  action  occurs  when  dry  sul- 
phuretted hydrogen  is  passed  into  a  solution  of  iodine  in  dry 
carbon  disulphide,  but  that  as  soon  as  water  is  added,  hy- 
driodic  acid  and  sulphur  are  produced.     The  reaction 
2H2S  +  2l2  =  4HI  +  S2 

(gaseous)    (solid)   (gaseous)  (solid) 

would  be  thermally  represented  as 

[2ff*S,  2l2]  =       4  \ff,  /]  -  2  [H\  8] 

=  —  24800  -  9200 
=  -  34,000. 

When  water  is  present,  the  reaction 

2H2S     +     2l2    =    4HI     +     S2 

(in  solution)  (in  solution)     (in  solution)       (solid) 

would  be  thermally  represented  as2 

[2H*SAq,  2l2Aq]  =  4  \H,  I,  Aq]  -  2  [//2,  S,  Aq] 
=  52,800-  18400 
=  34,400  +  . 

The  reaction  of  dry  sulphuretted  hydrogen  with  dry  iodine 
would  be  markedly  endothermic  ;  but  when  this  change  is  made 

1  Her.  2.  177;  and  Annalen  181.  145. 

-  No  notice  is  taken  in  these  thermal  expressions  of  the  change,  if  any,  which 
accompanies  the  decomposition  of  2!,  and  the  production  of  S2.  See  post,  pars. 
122,  132. 


254  THERMAL   METHODS.  [BOOK  I. 

one  of  a  series  the  thermal  value  of  which,  taken  as  a  whole, 
is  positive,  then  the  complete  cycle  of  change  proceeds  rapidly. 
But  the  more  concentrated  an  aqueous  solution  of  hydri- 
odic  acid  becomes  the  less  heat  is  there  produced  on  each 
addition  of  the  acid,  until  the  specific  gravity  of  the  liquid 
is  i'56,  after  which  no  more  heat  is  produced1 ;  the  liquid  is 
saturated.  If  therefore  the  hydriodic  acid  formed  in  the 
foregoing  reaction  is  allowed  to  accumulate  in  the  liquid,  no 
more  water  being  added,  a  point  will  be  reached  at  which  the 
sum  of  the  thermal  changes  is  equal  to  zero ;  at  this  point 
the  chemical  change  stops,  but  proceeds  again  on  the  addi- 
tion of  a  little  water.  It  is  possible  to  obtain  an  aqueous 
solution  of  hydriodic  acid  of  specific  gravity  r6/  ;  if  sulphur 
is  shaken  with  this  liquid  a  little  sulphuretted  hydrogen  and 
iodine  are  produced,  i.e.  the  change 

S2  +  4HI  =  2H2S   +   I2 

(solid)  (concentrated)  (solution)  (solution) 

proceeds  until  the  hydriodic  acid  becomes  reduced  to  specific 
gravity  1-56,  when  equilibrium  is  again  established. 

Portions  of  this  cycle  of  change  are  exothermic,  other 
portions  are  endothermic.  Variation  of  the  mass  of  one  of 
the  members  of  the  changing  system  determines  whether 
the  thermal  value  of  the  complete  change  shall  be  positive 
or  negative,  and  also  determines  the  direction  in  which  the 
change  shall  proceed.  This  reaction  may  be  taken  as  typical 
of  most  if  not  all  chemical  processes.  Such  processes  consist 
of  portions  having  positive  thermal  values  and  portions  having 
negative  values ;  small  variations  in  the  conditions  may 
determine  whether  the  process  as  a  whole  shall  belong  to  the 
class  of  exothermic  or  to  that  of  endothermic  changes. 

Too  much  stress  has  been  laid  by  one  school  of  chemists  on 
the  differences  between  exothermic  and  endothermic  changes. 
120  Direct  measurements  of  the  thermal  changes  which  ac- 
company chemical  changes  can  only  be  made  in  a  few 
simple  cases  ;  it  is  generally  necessary  to  have  recourse  to 
indirect  methods. 

1  This  liquid  contains  about  25  per  cent,  of  HI. 


CHAP.  IV.§  120]  CALCULATIONS.  255 

All  the  calculations  rest  on  the  following  deduction  from 
the  theory  of  energy. 

The  total  change  of  energy  which  accompanies  the  passage 
of  a  chemical  system  from  a  definite  initial  to  a  definite  final 
state  is  independent  of  the  intermediate  states. 

The  total  change  of  energy  is  of  course  measured  by  the 
heat  which  is  produced  or  disappears,  and  the  work  done  by, 
or  on,  the  system  in  its  passage  from  one  state  to  the  other. 
But  for  our  purpose  the  energy  given  out  in  forms  other  than 
that  of  heat  may  be  overlooked,  and  we  may  put  the  statement 
in  this  form  ;  the  total  thermal  change  during  a  chemical 
process  is  dependent  only  on  the  initial  and  final  states  of  the 
chemical  system  1. 

In  applying  this  statement,  it  is  necessary  to  arrange 
series  of  reactions  each  beginning  with  the  same  materials  in 
the  same  conditions  and  ending  with  the  same  products  under 
the  same  conditions  ;  all  the  processes  which  form  one  of  the 
cycles  of  change  must  be  capable  of  calorimetrical  measure- 
ment, and  all  the  processes  in  the  other  cycle,  except  that  one 
the  thermal  value  of  which  is  to  be  determined,  must  also  be 
capable  of  measurement  by  the  calorimeter :  if  this  be  done, 
it  follows  from  the  principle  just  stated  that  the  difference 
between  the  total  thermal  values  of  the  two  cycles  of  changes 
represents  the  thermal  value  of  that  special  portion  of  one  of 
the  cycles  which  it  is  wished  to  determine.  Each  cycle  may 
however  consist  of  various  parts,  so  that  it  is  sometimes  a 
little  difficult  to  unravel  all  the  changes,  and  to  find  that 
portion  of  one  cycle  the  thermal  value  of  which  has  to  be 
determined  by  calculation. 

I  shall  now  give  some  examples  to  shew  how  the  thermal 
values  of  various  chemical  changes  are  deduced  from  the 
results  of  experiments. 

A.  It  is  required  to  determine  the  thermal  value  of  the 
synthesis  of  CH2O2  from  C,  Ha,  and  O2. 

We  start  with  12  grams  of  carbon,  2  of  hydrogen,  and 
48  of  oxygen;  these  combine  to  form  18  grams  of  water, 

1  The  truth  of  this  generalisation  was  first  proved  experimentally  by  Hess  in 
\%V>(Pogg.  50.  38 si). 


256  THERMAL   METHODS.  [BOOK  I. 

and  44  grams  of  carbon  dioxide  (C  +  H2  +  O3  =  CO2  +  H2O). 
But  the  same  quantities  of  carbon,  hydrogen,  and  oxygen 
might  be  (theoretically)  combined  to  form  46  grams  of 
formic  acid  and  16  grams  of  oxygen,  and  the  formic  acid 
could  then  be  oxidised,  by  the  oxygen,  to  form  18  grams  of 
water  and  44  grams  of  carbon  dioxide.  Stated  in  formulae 
these  changes  are 

(i)  C  +  H2  +  02=CH2O2;        (2)  CH2O2  +  O  =  CO2  +  H20. 


The  following  are  the  thermal  values  of  the  different 
portions  of  these  changes  : 

[C,  02]  =  96,960+  :  [H*,  0]  =  68,360+  :  [CH2O2,  0]=  65,900  + 

but  [0,  02]  +  [//2,  0]  =  [0,  H\  02]  +  [CH202,  0]=  165,320+ 

.-.  [0,  H*,  02]=[C,  02]  +  [//2,  0]-[CH202,  0]=  99,420  +  . 

B.  A  rather  more  complicated  example  is  furnished  by 
the  determination  of  the  thermal  values  of  the  actions  (i) 
[H,  Br],  (2)  [H,  I]  ;  i.e.  of  the  reactions  whereby  HBr  and 
HI  are  conceived  to  be  formed  from  their  elements. 

(i)  [H,  Br].     The  data  are 

[If,  C/,  Aq]  =  39,300;  [HBr,  Aq]=  19,900*: 
therefore  assuming  that 

[If,  Br,  Aq]  =  [//,  C/,  Aq] 
it  follows  that 

[H,  Br]  =  39,300-  19,900=19,400. 

But  is  the  formation  of  an  aqueous  solution  of  HBr  from 
H,  Br,  and  water,  attended  with  the  same  thermal  change 
as  accompanies  the  formation  of  an  aqueous  solution  of  HC1 
from  H,  Cl,  and  water?  Or,  if  this  assumption  is  not 
justified  by  facts,  what  is  the  difference  between  the  thermal 
values  of  the  two  changes  ? 

Now,  in  the  first  place,  the  thermal  values  of  the  formation 
of  KC1  and  KBr  in  aqueous  solution  are  equal,  i.e. 

[KOHAq,  HClAq]  =  [KOHAq,  HBrAq]. 
1  When  no  +  or  —  sign  is  given  it  is  to  be  understood  that  heat  is  evolved. 


CH.  IV.  §120]  CALCULATIONS.  257 

But  the  replacement  of  Br  by  Cl  is  attended  with  production 
of  a  considerable  quantity  of  heat ;  the  data  here  are 

[KBrAq,  Cf]=  11,500. 

Now  if  we  analyse  this  change  we  find  that  the  thermal 
expression  when  expanded  becomes 

[K,  Cl,  Aq]  +  [5r,  Aq]  -  [K,  Br,  Aq]=  1 1,500 : 
but  [Br,  Aq]  =  50o: 

.'.  [K,  Cl,  Aq]  -  [K,  Br,  Aq]=  1 1,500  -  500=  1 1,000. 
That  is  to  say,  the  replacement  of  Br  by  Cl  in  aqueous  solu- 
tion is  represented  by  the  thermal  value  1 1 ,000  units,  and  as 
the  heat  of  neutralisation,  in  aqueous  solution,  of  KOH  by 
HC1  is  equal  to  that  of  KOH  by  HBr,  it  follows  that 

[H,  Br,  Aq]  =  [#,  Cl,  Aq]-  11,000=28,300  : 
and  as  {HBr,  Aq]  =  19,900,  it  follows  that  [H,  Br]  =  8,400. 

(2)     [H,  I].     The  data  are 

[H,  Cl,  Aq]  =  39,300  ;  [HI,  Aq]=  19,200. 

Now 

[KOHAq,  HIAq]  =  [KOHAq,  HClAqj-yo: 
also 

[KIAq,  C/]  =  26,2oo  (iodine  separating  as  solid): 

.'.  replacement  of  I  by  Cl  is  accompanied  by  production 
of  26,200  —  70  =  26,130  units  : 

.'.  [H,  I,  Aq]  =  [H,  Cl,  Aq]  -  26,130=  13,170 : 
and  as  [HI,  Aq]  =  1 9,200 

it  follows  that  [H,  I]=  13,170-  19,200 

=  -  6030. 

The  calculations  of  the  tieats  of  formation  of  compounds 
are  all  based  on  the  principle  we  are  now  discussing. 

C.  Thus,  required  the  heat  of  formation  of  methane 
(CH4).  We  start  with  the  two  systems  (i)  C  +  4#,  (2)  £//4. 
Each  is  completely  oxidised  to  the  same  final  products,  viz. 
CV98  +  2HSO;  the  difference  between  the  quantities  of  heat 
produced  in  these  two  changes  is  called  the  heat  of  formation 
of  CH4.  Thus, 

[0,  02]  =  96,900 :  2  [H2,  0}  =  1 36,800 :  sum  =  233,700 
but  [CH*,  Q4]  =  213,500 
/.  [0,  H*]=  20,200. 
M.C.  17 


258  THERMAL   METHODS.  [BOOK  I. 

As  it  is  important  that  a  definite  meaning  should  be 
attached  to  the  expression  'heat  of  formation,'  a  few  more 
examples  are  given. 

D.  Required  the  thermal  value  of  the  reaction  \H,  C,  N\ 
that  is,  of  the  reaction  whereby  HCN  may  be  conceived  to  be 
formed  from  its  elements. 

Data;  [C,  <92]  =  96,900:  $[f?2,  0]  =  34,200:  sum=  131,100  (N  is 
incombustible]  but  [CNH,  |O]=  159,500 

.-.  [G,N,HY=-   28,400. 

E.  Required  the  thermal  value  of  the  reaction  [TV2,  O\. 
Data  ;  the  reaction 

G  +  2NZO=2NZ  +  CO2  when  expanded  thermally  is 
[0,  2N*0]=[C,  0*\-2[N\  0]=  1  33,900: 
but  G  +  2Nz+O2=COz+'2N.t 
i.e.  [0,  iN\  O2]=[C,  O2 
.-.  2[N*,  O]=-  37,000 


F.  Required  the  thermal  value  of  the  reaction  [N,  O~\. 
Data;  CN+2NO=CO2  +  ^N,  or  in  thermal  notation 

[CN,  2NO]  =  [C,  O2]  -  [C,  N]-2  [N,  O]  =  1  74,600  : 
but  CN+O2=CO2  +  N,  or  in  thermal  notation 

[CN,  0*]  =  [C,  0*]-[C,  ^=130,900 
.-.  2[N,  O]=-  43,7oo: 
.-.     [IV,  0]=  -21,850. 

The  heat  of  formation  of  a  substance  will  of  course  vary 
according  as  the  substance  is  formed  in  the  gaseous,  liquid, 
or  solid,  state,  and  also  according  to  the  temperature  of 
formation.  The  following  examples  will  illustrate  this. 

G.  Required    the    thermal    value   of   the    formation    of 
aldehyde  from  its  elements,  i.e.  of  the  reaction  [C2,  //*,  O], 
when  the  aldehyde  is  (a)  liquid,  (b]  gaseous. 

(a)  Liquid:  data, 


but  2[C,  C>2]  +  2[/^2,  O]  =330,600 


=  55,100 
1  The  transference  of  N  from  the  molecule  N2  to  the  molecule  HCN  is  assumed 

to  be  accompanied  by  no  thermal  change.     See  post  par.  132. 

3  The  CO2  produced  is  gaseous;  the  heat  of  formation  of  liquid  CO2  is  un- 

known, 


CH.  IV.  §§  I2O,  I2l]  CALCULATIONS.  259 

(b)  Gaseous:  data, 

[C2tf*O,  6>5]  =  266,000;  and  2  [H-,  O}=  117,400: 
.-.  [Ca  +  #4  +  0  =  C2/f40]  =  45,200. 
H.     If  the  products  of  a  reaction  are  gaseous  and  are 

maintained  at  a  high  temperature,  it  becomes  necessary  to 

introduce   corrections   for    the   specific   heats,   and    heats   of 

vaporisation,  of  these  products,   into  the  calculation  of  the 

thermal  value  of  the  reaction. 

Thus,  required  the  thermal  value  of  the  reaction  [C*2//2,  O6] 

at  150°. 

Data,  C2//2  + 

at  ordinary  temperatures  (20°) 
\C*H\  O5]=2[C, 

but  thermal  capacity  of  2  gram-molecules  of  CO2  for  tem- 
perature-interval 20° — 150°  =   2482  units. 

/(«)  imol.liquidH2O20° — ioo°=i8x8o=   1440    „ 
thermal  capacity  of    (b)  heat  of  vaporisation  of  do.  at  100° 

i  gram-molecule -<          =  18x536-5  =  9657     „ 

of  H2O  \(c)  thermal  capacity  of  i  mol.  steam 

\         100° — 150°  =  i8x  50x0-4805  =     432     „ 


total=  1401 1  units. 


260  THERMAL   METHODS.  [BOOK  I. 

!X=  Cl  =  30,000  units. 
X=Br=  4,800  „  . 
X=I  =-18,000  „  . 

The  reverse  action  in  the  case  of  iodine,  viz. 

C2H3I  O2  +  HI=  C2H4O2  +  12 
is  represented  thermally  thus, 

[C2H3IO2,  /T/]  =  i8,ooo. 

This  action  occurs  provided  a  concentrated  aqueous  solu- 
tion of  hydriodic  acid  is  employed. 
Now  2# 


=  12,400. 
But  [2///,  Aq]  =  38,000  : 

hence  it  follows  that  in  the  decomposition  of  2//7  into  H^+  12 
in  dilute  solution  38,000—  12,400  =  25,600  units  of  heat  would 
disappear. 

These  thermal  numbers  shew  that  the  process  which 
is  accompanied  by  a  large  loss  of  energy  occurs,  whereas 
that  which  would  involve  gain  of  energy  to  the  system  does 
not  occur. 

But  why  does  a  concentrated  aqueous  solution  of  hydriodic 
acid  act  as  an  energetic  reducing  agent  ?  We  have  already 
learned  (p.  254)  that  little  or  no  heat  is  produced  during 
the  absorption  and  solution  of  gaseous  hydriodic  acid  by  a 
solution  of  that  gas  containing  about  20  —  25  per  cent,  of  HI  ; 
hence  a  concentrated  solution  of  this  compound  contains 
a  considerable  quantity  of  HI,  as  distinguished  from  HIAq. 
But  the  numbers  given  above  shew  that  HI  contains  much 
more  energy  than  HIAq  ;  hence  a  concentrated  aqueous 
solution  of  hydriodic  acid  is  much  more  energetic  than  a 
dilute  solution  of  the  same  compound1. 

The  following  tables2  contain  thermal  data  for  discussing 
the  action  of  sulphuretted  hydrogen  as  a  reagent  for  precipi- 
tating certain  metals  from  acid  solutions,  and  other  metals 
only  from  neutral  or  alkaline  solutions. 

1  See  Naumann,  Thermochemie,  495  and  501. 

2  See  Naumann,  loc.  cit.  505  —  510. 


CH.  IV.  §I2l]  CLASSIFICATION.  261 

TABLE  I. 

Base 


Reaction  CdO      PbO  CuO     HgO     T12O     Cu2O    Ag2O 
[Base  2HClAq,  )  , 

H2SAq]        J  (l)  27'3°°  29)2°°  3I'7°°  45'3°°  38}5°°  38'5°°  58'5°° 

^  2°'3°°  I5'4°°  IS'3°°  I9'°°°  27)5°°  I4>7°°  42'6°° 


(i)-(2)=  +  7,000  13,800  16,400  26,300  11,000  23,800  15,900 

TABLE  II. 

Base 

Reaction  Cdo"      PbO       CuO       HgO       T12O      Cu2O     Ag,6 

[Base,  tf2S]    (1)32,100   34,000   36,500    50,000    43,300   43,300   63,300 
[Base,  •zHCl\  (2)  55,000   50,000    50,000    53,500    62,200   49,300   77,200 

(i)-  (2)=  -22,900    16,000    13,500     3,500    18,900     6,000    13,900 

TABLE  III. 

Base 


Reaction  MnO.H2O  FeO.H2O  NiO.H2O  CoO.H2O  ZnO.H2O 

a2  t1)     10>7°°         I^6o°         l8'6o°         I7»4QO         18,600 


[Base  Aq,      )   . 

2HClAq]       J  (2)     23'00°        2I'4°°         22'6°° 


(l)  -  (2)=  -  12,300          6,800          4,000          3,700  1,700 

To  illustrate  the  application  of  these  data,  take  the  case 
of  cadmium. 

(1)  [CdO2HClAq,  H2SAq]  =  27,300: 

i.e.  the  thermal  change  which  occurs  when  aqueous  HSS  reacts 
on  a  dilute  solution  of  CdO  in  HC1  is  represented  by  the 
production  of  27,300  units. 

(2)  [CdO  Aq,  2HClAq]  =  20,300: 

i.e.  the  thermal  change  which  would  occur  if  CdO  in  aqueous 
solution  were  neutralised  by  a  dilute  solution  of  HC1  would 
be  represented  by  the  production  of  20,300  units.  The  former 
number  exceeds  the  latter  by  7,000,  .'.  the  action  of  H2S,  in 
solution,  on  CdO,  in  dilute  HC1  solution,  is  accompanied  by 
the  production  of  7,000  units  of  heat;  this  action  readily 
occurs.  But 

[CdO,  H*S]  =  32,100  ;  and  [CdO,  2/TC7]  =  55,000: 
i.e.  the  formation  of  CdS,  by  the  action  of  gaseous  H2S  on  solid 
CdO,  is  accompanied  by  the  production  of  22,900  units  of 


262  THERMAL   METHODS.  [BOOK  I. 

heat  less  than  attends  the  action  of  gaseous  HC1  on  CdO  ; 
now  solid  CdS  is  decomposed  by  gaseous  HC1  with  formation 
of  CdCl2. 

Moreover  the  numbers 

[2HCt,  Aq]  =  34,600;  whereas  [H2S,  Aq]  =  4,800 

shew,  that  gaseous  hydrochloric  acid  possesses  an  excess  of 
energy  measured  by  about  34,000  thermal  units  above  what 
it  possesses  when  in  dilute  solution,  whereas  the  excess  of 
energy  of  an  equivalent  mass  of  gaseous  H2S  above  that 
possessed  by  H2SAq  is  measured  by  about  5000  thermal 
units.  But  the  more  concentrated  an  aqueous  solution  of 
hydrochloric  acid,  the  less  is  the  quantity  of  heat  produced 
by  adding  hydrochloric  acid  gas  to  that  solution  ;  in  other 
words,  a  concentrated  aqueous  solution  of  this  acid  is  nearly 
as  energetic  a  reagent,  provided  it  is  used  in  sufficient 
quantity,  as  gaseous  hydrochloric  acid.  Hence  we  should 
conclude,  and  our  conclusion  is  verified  by  experiment, 
that  cadmium  sulphide  will  be  decomposed  by  concentrated 
aqueous  hydrochloric  acid. 

The  case  of  antimony  is  especially  interesting. 

Antimony  sulphide  is  decomposed  by  aqueous  hydrochlo- 
ric acid  of  greater  concentration  than  HC1.6H2O;  but  if  more 
water  than  this  is  present,  antimony  chloride  is  decomposed 
by  sulphuretted  hydrogen.  Hence  the  two  reactions 


may  occur  until  a  state  of  equilibrium  is  established,  which 
is  conditioned  by  the  relative  energies  of  the  components, 
and  this  again  is  conditioned  by  the  relative  masses  of  these 
components,  temperature  being  constant  throughout. 
122  We  have  been  accustomed  to  regard  most  processes  of 
chemical  change  as  consisting  of  two  parts,  (i)  decomposition 
of  the  molecules  forming  the  initial  system,  (2)  rearrangement 
of  the  atoms  thus  produced  to  form  the  new  molecules  which 
compose  the  final  system.  The  first  part  of  a  change,  as 
thus  regarded,  must  be  accompanied  by  gain  of  energy  to 
the  entire  system,  and  the  latter  part  by  loss  of  energy.  The 
gain  may  exceed  the  loss,  or  vice  versa  ;  the  process  as  a 


CH.  IV.  §§  122,  123]       ATOMS   AND   MOLECULES.  263 

whole  may  be  endothermic  or  exothermic.  In  the  preceding 
paragraphs  of  this  section  no  attempt  has  been  made  to 
separate  the  thermal  values  of  these  two  parts  of  any  change ; 
the  numbers  given  in  these  paragraphs  represent  the  algebraic 
sums  of  two  or  more  quantities.  In  some  cases  the  chemical 
changes  are  represented  in  formulae  which  are  undoubtedly 
molecular,  but  in  most  cases  we  have  dealt  with  solid  or 
liquid  substances,  and  the  thermal  values  assigned  to  the 
various  changes  must  therefore  generally  be  regarded  as  only 
measuring  the  quantities  of  heat  produced  or  used  during 
the  reactions,  as  defined  in  the  equations,  between  those 
masses  of  the  various  chemical  substances  which  are  ex- 
pressed by  their  formulae  when  read  in  grams. 

But  if  relative  measurements  of  the  gains  of  energy  which 
accompany  the  formation  of  atomic,  from  molecular,  systems, 
could  be  obtained,  much  light  would  certainly  be  thrown  on 
many  questions  which  have  been  discussed  or  alluded  to  in 
preceding  chapters. 
123  Thomsen1  has  attempted  to  calculate  the  quantity  of  heat 
required  to  separate  the  molecule  of  carbon,  assumed  to  be  di- 
atomic, into  atoms ;  his  results  and  methods  cannot  be  accepted 
as  conclusive2.  The  'heat  of  dissociation  '  of  a  carbon  atom  is 
supposed  by  Thomsen  to  be  equal  to  about  37,000  gram-units. 

E.  Wiedemann3  has  measured  the  heat  required  to  change 
the  'band  spectrum'  of  hydrogen  into  the  'line  spectrum'; 
and,  on  the  assumption  that  the  '  line  spectrum '  is  associated 
with  vibrations  of  atoms  and  the  '  band  spectrum '  with 
vibrations  of  molecules,  he  has  calculated  that  about  128,000 
gram-units  of  heat  are  required  in  order  to  separate  I  gram- 
molecule  of  hydrogen  into  its  constituent  atoms ;  and  that 
a  greater  quantity  of  heat  than  this  is  required  in  the  case  of 
the  molecule  of  nitrogen. 

Thomsen  and  Wiedemann  have  shewn  that  more  energy 
is  almost  certainly  associated  with  a  mass  of  hydrogen, 

1  Ber.  13.  1321  and  1388.     Do.  15.  328.    See  also  Thermochemische  Untersuch- 
ungen,  2.  101  et  seq. 

2  See  The  Elements  of  Thermal  Chemistry >  pars.  73 — 75:  see  also  post  par.  134. 

3  Wied.  Ann.  C.  500,  and  do.  18.  509. 


264  THERMAL   METHODS.  [BOOK  I. 

nitrogen,  or  gaseous  carbon,  when  the  greater  part  of  the 
matter  is  in  the  state  of  atoms  than  when  in  the  state  of 
molecules  ;  in  other  words,  their  investigations  furnish  physi- 
cal evidence  in  favour  of  the  generally  adopted  explanation 
of  nascent  actions. 

124  Some  of  the  reactions  of  metals  with  acids  were  considered 
in  Chap.  II.  pars.  42  to  44.  Thermal  measurements  help  to 
elucidate  these  actions. 

If  the  heats  of  formation  in  aqueous  solution  of  the  sul- 
phates of  silver,  thallium,  copper,  cadmium,  mercury,  nickel, 
cobalt,  iron,  manganese,  and  zinc,  are  compared  with  the 
heat  of  formation  of  sulphuric  acid  in  aqueous  solution,  it  is 
found  that  the  former  values  are  greater  than  the  latter  except 
in  the  cases  of  copper  and  silver  :  i.e.  for  the  heavy  metals 

[M(or  M2),  0\  S0\  Aq]  >  \H\  O\  SO2,  Aq], 

except  when  M  =  Cu  or  M2  =  Ag2  ;  hence  we  might  expect 
the  heavy  metals,  except  copper  and  silver,  to  decompose 
dilute  sulphuric  acid  with  evolution  of  hydrogen. 

When  M2  =  T12  .the  positive  value  of  the  difference  in 
question  is  not  large  (1,900  units);  the  action  between  this 
metal  and  dilute  sulphuric  acid  does  not  proceed  rapidly. 
But  when  the  acid  is  concentrated  action  is  more  energetic  ; 
now  inasmuch  as  the  heat  of  solution  of  H2SO4  is  large 

[H2SO4,  Aq]=i7,ooo 

it  follows  that  a  given  mass  of  concentrated  sulphuric 
acid  contains  considerably  more  energy  than  the  same 
mass  of  dilute  acid,  and  hence  the  concentrated  acid  will 
probably  be  less  chemically  stable  than  the  dilute.  The 
reaction  of  thallium  with  the  concentrated  acid  results  in 
the  production  of  some  sulphur  dioxide.  Now  the  change 
H8SO4+  H2  =  SO2+2H2O  (assuming  that  this  expresses  the 
origin  of  the  sulphur  dioxide)  is  accompanied  by  the  pro- 
duction of  14,900  units  of  heat.  This  change  is  represented 
thermally  thus, 

[H2S04,  ^  =  [ 


If  the  temperature  is  raised  the  acid  becomes  more  con- 
centrated, and  at  a  certain  stage  sulphuretted  hydrogen  is 


CH.  IV.  §  1  24]         ACTION   OF   ACIDS   ON    METALS.  265 

evolved.     This  action  is  thermally  probable,  because 

£H2S04+H2  =  i 
when  expanded  thermally,  is 


=  23,700  units. 

A  similar  treatment  of  the  action  of  copper  on  sulphuric 
acid  shews  that  this  metal  would  probably  not  decompose 
the  acid  when  dilute,  but  that  the  metal  might  be  expected 
to  react  slowly  with  concentrated  acid,  provided  one  of  the 
products  were  sulphur  dioxide  ;  because 


when  expanded  thermally,  is 

[Cu,  2H2S04]=[Cu,  S0\  0*}  +  2[ff*,  O\-2\H\  O\  SO2] 
=  4,500  units. 

The  quantity  of  heat  set  free  in  this  action  will  in  reality 
considerably  exceed  5000  units,  because  heat  will  be  produced 
by  the  action  between  the  sulphuric  acid  and  the  water  formed 
in  the  change  ;  the  amount  of  heat  thus  liberated  may  amount 
to  as  much  as  8,000  or  9,000  units  per  gram-molecule  of  water. 

The  fact  that  the  mutual  action  of  sulphuric  acid  and 
water  is  accompanied  by  the  production  of  much  heat  compli- 
cates such  calculations  as  those  given  above.  The  relations 
between  the  masses  of  H2SO4  and  H8O  employed  will  cer- 
tainly condition  the  direction  and  progress  of  the  change. 
Starting  with  the  system  HsSO4  +  £cH2O  +  #H2,  for  a  certain 
concentration  of  acid  the  final  configuration  will  be  SO2  and 
H2O,  for  another  concentration  of  acid  it  will  rather  be  H2S 
and  H2O,  or  SO2,  H2S,  and  H2O.  The  action  will  also  of 
course  be  conditioned  by  temperature. 

If  the  foregoing  considerations  are  correct,  it  follows  that 
any  metal  which  reacts  with  dilute  sulphuric  acid  with  evolu- 
tion of  hydrogen,  might  fairly  be  expected  to  react  with  the 
same  acid  to  produce  sulphuretted  hydrogen  or  sulphur 
dioxide  under  certain  conditions  of  temperature  and  con- 
centration ;  zinc  and  tin  certainly  do  produce  both  of  these 
gases  by  their  action  on  hot  concentrated  sulphuric  acid1. 

1  See  p.  103.  The  subject  of  the  reactions  of  metals  with  acids  is  treated  from 
the  thermal  standpoint  in  pars.  120  —  122  of  The  Elements  of  Thermal  Chemistry. 


266  THERMAL   METHODS.  [BOOK  I. 

125  From  what  we  have  learned  regarding  atomic  and  mole- 
cular systems,  and   from  a  consideration    of  the   preceding 
paragraphs  of  this  section,  it  follows  almost  necessarily  that 
the  change  from  one  allotropic  modification  of  an  element  to 
another  must  be  attended  by  production  or  disappearance  of 
heat.     A  few  thermal  measurements  are  given  here  to  shew 
that  this  conclusion  is  fully  justified  by  facts. 

A.  [P2,  <95]  =  369,ioo  units  when  P2  is  62  grams  of  ordinary 

phosphorus  (Pa); 
[P2,  0*]  =  326,800  units  when  P2  is  62  grams  of  amorphous 

phosphorus  (P/s); 

/,  the  change  of  Pa  to  P^  =  21,150  units  of  heat. 

In  the  oxidation  of  31  grams  Pa  to  H3PO4  in  aqueous  solution  by  hypo- 
chlorous  acid,  209,500  thermal  units  are  produced ; 

in  the  oxidation  of  31  grams  PB  to  H3PO4  in  aqueous  solution  by  hypo- 
chlorous  acid,  181,200  thermal  units  are  produced  ; 

/.  the  change  of  Pa  to  P^  =  28,300  units  of  heat. 
Hence  mean  value  of  this  change  =  24,725  gram-units. 

B.  [2(?^=36>2]  =  59,20o  units  of  heat;  that  is  to  say 

the  separation  of  2  gram-molecules  of  ozone  (O3)  into  3  gram-molecules 
of  oxygen  (O2)  is  attended  by  the  production  of  59,200  units  of  heat. 

The  comparative  thermal  instability  of  the  molecule  O8 
helps  us  to  understand  why  ozone  is  so  much  more  active  as 
an  oxidising  agent  than  ordinary  oxygen1. 

126  Too  little  has  as  yet  been  done  to  allow  of  the  application 
of  thermal  measurements  to  the  classification  of  the  elements 
in  any  but  a  very  general  way. 

The  relations  existing  between  the  members  of  a  group  of 
elements  are  sometimes  summarised  in  the  thermal  values  of 
comparable  reactions  undergone  by  these  elements.  Thus, 
(see  table  p.  225)  taking  MendelejefFs  Group  II.  we  have, 

Series. 


468  3       5  7        9         ii 

Ca      Sr     Ba  Mg     Zn  Cd       -        Hg 

atomic  weights  40       87     137  24       65  112  200 

1  According  to  van  der  Meulen  (Ber.   16.    1853)  the  thermal   value  of  the 
change  in  question,  2O3=3O2,  is  about  68,000  units. 


CH.IV.  §§125  —  127]    CLASSIFICATION   OF  ELEMENTS.  267 

The  heats  of  formation  in  aqueous  solution  of  the  haloid 
salts  of  these  metals  are  arranged  in  the  following  table  (data 
from  Naumann's  book)  : 

[M,  Cl\  Aq]  [M,  Br\  Aq]            [M,  F,  Aq] 

Ca               187,600  165,800                   I35»3°o 

Sr                i95)7oo  173,800                    H3.4OO 

Ba                196,300  174,400                    144,000 

Mg  186,900  165,000  134,600 

Zn  112,800  90,900  60,500 

Cd  96,3oo  74,400  44,000 


Hg 

Hence  we  conclude  that  in  each  case  the  value  for 
Ba  >  Sr  >  Ca  >  Mg,  and  for  Mg  >  Zn  >  Cd  >  Hg.  In  other 
words,  the  thermal  value  of  the  change  [M,  X  *,  Aq]  increases 
as  the  atomic  weight  of  M  increases,  when  M  is  a  member  of 
an  even  series  belonging  to  Group  II.  but  decreases  as  the 
atomic  weight  of  M  increases,  when  M  is  a  member  of  an  odd 
series  of  the  same  group.  The  difference  between  the  values 
of  [M,  X*,  Aq]  for  each  pair  of  elements  is  nearly  constant. 

Thus 

X=Cl  X=Br  X=I 

Ba  -  Sr  =      600  600  600 

Sr  -Ca=  8,100  8,000  8,100 

Ca  -  Mg  =      700  800  700 

Mg-Zn  =74,100  74,ioo  74,ioo 

Zn  -Cd  =  16,500  16,500  16,500 

Cd-Hg=  36,400  ?  ? 

The  close  relationship  of  magnesium  to  calcium,  and  also 
its  relations  to  barium  and  strontium,  and  the  comparatively 
feebly  marked  relations  existing  between  magnesium,  zinc, 
cadmium,  and  mercury,  are  brought  into  forcible  relief  by 
these  numbers1. 

127        The  comparative  study  of  classes  of  compounds,  no  less 
than  that  of  classes  of  elements,  has  already  been  considerably 

1  Attention  has  already  been  drawn  to  the  fact  that  there  exists  a  well-marked 
connexion  of  a  periodic  character  between  the  atomic  weights  of  the  elements 
and  their  heats  of  combination  with  chlorine,  bromine,  and  iodine.  (See  ante, 
par.  109.) 


268  THERMAL   METHODS.  [BOOK  I. 

advanced  by  the  application  of  thermal  methods.  Thus,  a 
study  of  some  of  the  thermal  relations  of  the  hydracids  and 
oxyacids  of  the  halogens  helps  towards  a  classification  of  the 
latter  group  of  acids. 

The  close  thermal  analogy  between  the  hydracids  in 
question  is  exhibited  by  these,  among  other,  numbers ; 

\HX,  Aq]  [HXAq,  NaOHAq] 

X=Cl  =  17,400  X  =  0=13,700 

X= £7=19,900  X  =  Br=  13,700 

X=I   =19,200  X=I    =13,700. 

When  we  compare  the  heats  of  formation  of  these  acids 
in  aqueous  solution,  we  find  that  the  value  of  this  constant 
for  each  acid  decreases  as  the  atomic  weight  of  the  halogen 

increases :  thus 

[H,  X,  Aq] 
X=Cl=  39,300 
X=  £r=  28,400 
X=I    =13,200. 

The  three  oxyacids  which  correspond  in  composition  to  the 
three  hydracids  are  HC1O3,  HBrO8,  and  HIO3.  The  following 
numbers  shew  that,  in  some  respects  at  any  rate,  the  thermal 
relations  between  HC1O3  and  HBrOs  are  analogous  to  those 
between  HC1  and  HBr  :— 

[H,  X,  O3,  Aq] 

x=  a  =  23)9oo 

X=ffr=  12,400 

hence  the  difference,  [H,  Cl,  Aq]  -  [H,  Br,  Aq]  is  approxi- 
mately equal  to  the  difference  [H,  Cl,  0s,  Aq] -[H, Br,  O\  Aq,] 
We  might  provisionally  conclude  from  these  data  that  the 
difference  between  the  heats  of  formation,  in  aqueous  solu- 
tions, of  chloric  and  iodic  acids,  would  probably  be  nearly  the 
same  as  the  difference  between  the  heats  of  formation,  under 
the  same  conditions,  of  hydrochloric  and  hydriodic  acids. 
The  value  of  the  second  difference  is  26,100;  hence,  on  this 
supposition,  the  first  difference  should  be  about  26,000.  Now, 

[//,  CY,  03,  Aq]  =  23,9oo; 
.-.[#,!,  0s,  Aq]=- 2,100. 
But  experiment  shews  that 

[If,  I,  O3,Aq]=  +  55,700. 


CH.  IV.  §§  127,  128]      CLASSIFICATION   OF   ACIDS.  269 

Hence  it  is  evident  that  iodic  acid  differs  in  the  most 
marked  manner  from  bromic  and  chloric  acids.  This  difference 
is  accentuated  in  the  numbers  expressing  the  heats  of  forma- 
tion of  these  three  acids  from  the  three  hydracids :  thus, 

[HXAq,  0*} 
X  =  C1=  -15,400. 
X  =  Br=  -15,900. 
X=I    =+42,600. 

But  it  is  to  be  remembered  that  gaseous  chlorine  and 
bromine  and  solid  iodine  are  employed  in  the  calculations1. 
128  A  comparison  of  the  mutual  thermal  actions  of  acids  and 
bases  throws  considerable  light  on  the  classification  of  the 
substances  which  are  included  under  these  terms.  The  first 
volume  of  Thomsen's  Untersuchungen  is  devoted  to  a  con- 
sideration of  this  subject. 

'  Heat  of  neutralisation  of  an  acid  by  a  base '  is  defined  as, 
the  quantity  of  heat  produced  on  mixing  equivalent  quantities, 
in  grams,  of  the  acid  and  base,  in  dilute  aqueous  solutions, 
the  products  of  the  action  being  also  soluble  in  water. 

Thomsen  employs  a  solution  of  2NaOH  in  about  200  H2O 
(grams),  and  adds  the  acid  solution  diluted  to  a  similar  degree, 
temperature  being  18° — 19°;  in  other  words  he  determines  the 
thermal  value  of  the  change 

[2NaOHAq,  2 HXAq]  in  the  case  of  a  monobasic  acid, 
[2NaOHAq,  H2XAq]  „  dibasic  „ 

[2NaOHAq,  |H3XAq]  „  tribasic 

[2NaOHAq,  £H4XAq]  „  tetrabasic      „ 

(X  =  acid  radicle) 

Most  of  the  general  conclusions  drawn  by  Thomsen,  and 
others,  belong  more  to  chemical  kinetics  than  to  statics,  but 
some  of  the  generalisations  may  fitly  be  introduced  here2. 

The  commoner  acids  may  be  broadly  divided  into  four 
groups  according  to  the  values  of  their  heats  of  neutralisation, 
as  thus  defined. 

1  The  application  of  thermal  data  to  the  classification  of  elements  and  com- 
pounds is  considered  more  fully  in  section  4  of  Chap.  in.  of  The  Elements  of 
Thermal  Chemistry. 

2  See  especially  for  more  details  Thomsen,  he.  dt.  1.  293 — 309,  and  422 — 449. 


2/O  THERMAL   METHODS.  [BOOK  I. 

I.  Those    acids    which    have   a    heat    of   neutralisation 
approximately  equal  to  20,000  gram-units  : — 

HN02,     HC10,     H2B204,     H2CO3  &c. 

II.  Those   acids   which   have   a   heat   of  neutralisation 
approximately  equal  to  25,000  gram-units  : — 

H2CrO4,     C2H4(C02H)2,     CH,CHOH(CO2H)2  &c. 

III.  Acids  the  heat  of  neutralisation  of  which  is  equal 
to  about  27,000  gram-units  : — 

HC1,     HBr,     HI,     HC1O3,     HBrO3,     HIO3,     HNO3,     H2S2O3, 
H2SiF6,     H.C02H,     CH3.CO2H  &c. 

Most  of  the  acids  belong  to  this  class. 

IV.  Acids  having  a  heat  of  neutralisation  greater  than 
27,000  units,  and  varying  from  28,000  to  32,500  units  ; — 

CH2C1.CO2H,     CHC12.CO2H,     CC13.CO2H,     H2C2O4,    H3PO3,    H2SO3, 
H2SO4,     H2Se04,     HF,     HPO3  &c. 

A  few  acids  have  heats  of  neutralisation  less  than  20,000 
units. 

The  basicity  of  an  acid  may  be  determined  by  thermal 
methods.  One  gram-molecule  of  the  acid  in  dilute  aqueous 
solution  is  mixed  with  \,  £,  |,  I,  2,  &c.  gram-molecules  of 
caustic  soda  also  in  dilute  solution,  and  the  heat  produced  in 
the  reactions  is  measured.  (The  ordinary  formulae  NaOH, 
H2SO4,  &c.  are  here  assumed,  for  the  sake  of  convenience  of 
nomenclature,  to  be  molecular.)  Comparing  in  this  way  HC1, 
H2SO4,  and  CBH8O7  (citric  acid),  we  have  this  result ; — 

[HClAq,  £NaOHAq]  =  about  6,000  [H2SO4Aq,  £NaOHAq]  =  about  7,000 
[HClAq,  NaOHAq]=  „  13,500  [H2SO4Aq,  NaOHAq]=  „  14,500 
[HClAq,  2NaOHAq]  =  „  13,500  [H2SO4Aq,  2NaOHAq]=:  „  31,000 

[H2S04Aq,  3NaOHAq]  =  „  31,000 

[C6H8O7Aq,     NaOHAq]=  12,400 

[C6H8O7Aq,  2NaOHAq]  =  24,800 

[C6H8O7Aq,  3NaOHAq]  =  38,000 

[C6H8O7Aq,  4NaOHAq]  =  38,000. 

Hence  we  conclude  that  HC1  is  a  monobasic,  H2SO4  a 
dibasic,  and  C6H8O7  a  tribasic,  acid. 

The  polybasic  acids  may  also  be  classified  in  accordance 
with  the  thermal  value  of  the  action  of  each  gram-molecule 


CH.  IV.  §128]  CLASSIFICATION   OF   ACIDS.  2/1 

of  soda  with  one  gram-molecule  of  acid.  Thus,  comparing 
oxalic  with  sulphurous  acid,  we  find  the  difference  between 
the  quantities  of  heat  produced  during  the  action  of  the  first 
and  second  molecules  of  soda,  in  the  case  of  oxalic  acid  to 
be  600,  and  in  that  of  sulphurous  acid  to  be  2750:  the  data 
are, 

Difference. 

[H2C204Aq,       NaOHAq]=i3,840\  /[H2SO3Aq,      NaOHAq]=  15,850 

[HNaC204Aq,  NaOHAq]=  14,440^  '    \[HNaSO3Aq,  NaOHAq]=  13,100. 

Thomsen1  divides  the  dibasic  acids  which  he  has  examined 
into  three  groups: — 

I.  Those  in  the  neutralisation  of  which  each  molecule 
of  soda  has  the  same  thermal  value:  this  group  is  at  present 
represented  by  H2SiF6>  and  H2PtCl62. 

II.  Those  in  the  neutralisation  of  which  the  first  mole- 
cule of  soda  has  a  smaller  thermal  value  than  the  second, 
the  difference  between  the  two  values  varying  from  450  to 
1900   units :   this   group   contains  the  acids  H2SO4,  H2SeO4, 
H2C204,  and  HrC4H4Or 

III.  Those  in  the  neutralisation  of  which  the  first  mole- 
cule of  soda  has  a  larger  thermal  value  than  the  second,  the 
difference  between  the  two  values  varying  from  1850  to  2750 
units:  the  acids  in  this  group  are  H2SO3,  H2SeO8,  H2CO3,  and 
H2B2O4;  H2CrO4,   H2PHO3,  and  C2H4(CO2H)2  also  probably 
belong  to  this  group,  although  the  differences  between  the 
thermal  values  of  the  first  and  second  molecule  of  soda  are 
smaller  in  the  case   of  these   acids   than   of  those   already 
mentioned. 

Thomsen  suggests  (I.  pp.  304-5)  that  the  foregoing  classi- 
fication of  dibasic  and  tribasic  acids  may  be  summarised  in 
these  typical  formulae: — 

Dibasic  Acids. 

Acid  of  Group  I.        Typical  formula  RH2          e.g.  SiF6.  H2 ; 
II.  „  R(OH)2     e.g.  S02(OH)2; 

III.  „  R(OH)H  e.g.  SO2(OH)H. 

1  loc.  cit.  1.  302 — 306. 

2  But  it  seems  doubtful  whether  the  numbers  obtained  by  Thomsen  really 
represent  the  neutralisation  of  this  acid.     See  Thermochtmische  Untersuchnngen, 
I.  229. 


2/2  THERMAL   METHODS.  [BOOK  I. 

Tribasic  Acids. 

Acid  of  Group  II.       Typical  formula  R(OH)3     e.g.  C4H5O4(OH)3; 
III.  „  HR(OH)H  e.g.  HPO3(OH)H. 

The  '  heat  of  neutralisation  of  a  base '  is  defined  by 
Thomsen1  to  be  the  thermal  value  of  the  change  which  occurs 
when  equivalent  quantities  of  base  and  acid  react  in  dilute 
aqueous  solution,  the  products  of  the  action  being  also  soluble 
in  water.  A  dilute  solution  of  one  gram-molecule  of  sulphuric 
acid  (i.e.  the  amount  of  acid,  in  grams,  expressed  by  the 
formula  H2SO4)  is  employed;  temperature  being  18° — 19°. 

In  other  words,  Thomsen  measures  the  thermal  values  of 
the  following  reactions: — 

[H2SO4Aq,  2MOHAq      or  2NX3Aq]  in  the  case  of  a  mono-acid  base, 
[H2SO4Aq,  M(OH)2Aq    or     N2X6Aq]  „  di-acid     „ 

[H2SO4Aq,  f  M(OH)3Aq  or  §N3X9Aq]  „  tri-acid     „ 

[H2SO4Aq,  JM(OH)4Aq  or  iN*X12Aq]  „  tetracid     „ 

(X  =  H,  or  a  radicle  CMH2n+1) 

The  bases  which  are  soluble  in  water  may  be  divided  into 
two  thermal  groups  : — 

I.  The  group  of  the  hydrates  or  hydroxides,  represented 
by  NaOH  and  KOH. 

II.  The  group  of  the  anhydrous  bases,  represented  by 
NH3. 

The  first  group  comprises  LiOH,  NaOH,  KOH,  and 
T1OH;  Ca(OH)2,  Sr(OH)2,  and  Ba(OH)2;  N(CH3)4OH, 
(C2H5)3S.OH,  and  Pt  (NH8)4  (OH)2:  the  mean  value  of  the 
change  [H2SO4Aq,  2MOHAq  (or  M(OH)2Aq)]  is  equal  to 
31,350  units,  when  M(OH)  or  M(OH)2  is  one  of  the  bases  of 
this  group. 

The  second  group  comprises  NH3  and  the  amines  of  the 
form  NH2(CBH2n+1)  and  NH(CnH2n+])2:  the  mean  value  of 
the  change  [H2SO4Aq,  2NX3Aq]  is  equal  to  28,200,  when 
NX3  is  one  of  the  bases  of  this  group. 

Substitution  of  negative  radicles  for  H  in  NH3  causes  a  con- 
siderable decrease  in  the  heat  of  neutralisation  of  the  base ;  thus, 
[2NH2(C6H6)Aq,  H2SO4Aq]=i5,5oo, 
[2NH2(C7H7)Aq,  H2SO4Aq]=  15,200 ; 
[2NH2OHAq,  H2SO4Aq]      =21,600. 
1  See  especially  loc,  cit.  1.  422 — 449. 


CH.IV.  §128]  CLASSIFICATION   OF   BASES.  273 

When  CO  is  substituted  for  H2  in  2NH8,  the  heat  of 
neutralisation  of  the  product  [(NH2)2CO]  is  almost  nil. 

Measurements  of  the  quantities  of  heat  produced  during 
the  reactions  of  acids  with  those  bases  which  are  insoluble  in 
water  shew  great  irregularities.  The  true  heats  of  neutrali- 
sation of  these  bases  cannot  be  determined.  But  from  the 
analogies  between  the  hydrates  of  barium,  strontium,  and 
calcium,  and  those  of  magnesium,  zinc,  and  manganese1, 
Thomsen  concludes  that  the  heats  of  neutralisation  of  the 
bases  of  the  magnesian  class  are  equal  to  those  of  the  bases 
of  the  akaline  earth  metals;  but  as  the  heats  of  neutralisation 
of  the  latter  and  of  the  alkalis  are  equal,  Thomsen  argues 
that  the  mean  value  of  the  heat  of  neutralisation  of  M(OH)2, 
when  M  =  Mg,  Mn,  Ni,  Co,  Fe,  Cd,  Zn,  or  Cu,  is  31,350  units. 

From  what  has  been  said  regarding  the  classification  of 
acids  in  accordance  with  their  heats  of  neutralisation2,  it 
will  be  apparent  that  if  2HClAq  is  substituted  for  H2SO4Aq 
in  the  preceding  reactions,  the  mean  heats  of  neutralisation  of 
the  two  groups  of  bases  will  be  represented  by  numbers 
smaller  than  31,350  and  28,200  respectively. 

The  identity  of  the  numbers  expressing  the  heats  of 
neutralisation  of  bases  of  such  different  composition  as  KOH 
and  Pt(NH3)4(OH)2  points  to  the  possibility  of  connecting 
similar  changes  of  energy  with  similarity  of  chemical  type, 
maintained  through  series  of  more  or  less  unlike  individuals. 
The  heats  of  neutralisation  of  the  bases  MX3  also  point 
to  the  existence  of  a  relation  between  change  of  energy  and 
composition  ;  but  the  influence  of  the  structure  of  the  indi- 
vidual substance  is  shewn  in  the  small  values  obtained  for 
NH2(C6H5)  and  NH2(C7H7),  in  which,  although  the  chemical 
type  is  maintained,  the  typical  thermal  value  is  widely  de- 
parted from. 

The  quantity  of  heat  produced  in  the  reaction  [2MOHAq, 
HXAq]  when  M  =  K,  Na,  &c.  is  nearly  constant,  whether 
X  =  C1,  Br,  or  I;  but  the  value  of  the  reaction  [PbO.H2O, 
HXAq],  or  [T12O.H8O,  HXAq]  &c.  differs  very  considerably 

1  See  Thomsen,  loc.  cit.  1.  435 — 440. 

2  See  ante,  p.  270. 

M.C.  1 8 


2/4  THERMAL   METHODS.  [BOOK  I. 

according  as  X  =  Cl,  Br,  or  I.  In  the  reaction  with  PbO.H2O, 
the  thermal  value  is  greatest  for  HIAq,  and  least  for  HClAq. 
Now  in  the  reactions  just  mentioned,  haloid  salts  are  produced 
which  are  only  slightly  soluble :  if  the  heats  of  solution  of 
these  salts  are  added  to  the  values  of  the  apparent  heats  of 
neutralisation  of  the  bases,  it  is  found  that  the  true  heats  of 
neutralisation  of  PbO.H2O,  T12O.H2O  &c.  are  represented  by 
the  same  number,  whether  HClAq,  HBrAq,  or  HIAq  is  the 
acid  employed.  If  it  is  granted  that  the  true  heats  of 
neutralisation  of  these  acids  are  the  same  for  other  bases 
which  form  insoluble  haloid  salts,  it  becomes  possible  to 
calculate  the  heats  of  solution  of  these  salts.  Thomsen 
has  done  this  for  PbCl2,  PbBr^,  PbI2,  AgCl,  &c.,  and,  carrying 
out  the  same  method,  he  has  even  given  a  value  for  the  heat 
of  solution  of  barium  sulphate. 

Thomsen's  investigation  of  the  heats  of  neutralisation  of 
acids  and  bases  serves  to  shew  the  complexity  of  many  of 
the  reactions  to  which  thermal  values  are  assigned,  and  also 
the  necessity  of  making  all  the  conditions  of  the  changes  we 
wish  to  study  as  exactly  comparable  as  possible.  At  the 
same  time  it  illustrates  one  of  the  dangers  which  beset  the 
employment  of  thermal  methods  in  chemistry,  the  danger 
namely  of  theorising  regarding  chemical  changes  which  do  not 
occur,  and  of  speculating  about  chemical  compounds  which 
have  no  existence1. 

129  The  primary  aim  of  thermal  chemistry  was  stated  in 
par.  117  to  be  the  measurement  of  the  differences  between 
the  quantities  of  energy  possessed  by  chemical  systems  when 
in  certain  definite  initial  and  final  states;  the  basis  of  these 
measurements  being  the  deduction  from  the  general  theory 
of  energy  which  states,  that  the  total  loss  of  energy  during 
the  passage  of  a  chemical  system  from  a  definite  initial  to 
a  definite  final  state  is  independent  of  the  intermediate 
states. 

The  application  of  this  generalisation  was  illustrated  in 
par.  1 20;  but  we  may  now  examine  a  little  more  closely  the 

1  Section  2,  of  Chap.  III.  of  The  Elements  of  Thermal  Chemistry  is  devoted  to 
the  consideration  of  neutralisation-phenomena. 


CH.  IV.  §§  129,  130]   THERMAL  AND  CHEMICAL  CHANGES.     2/5 

connexion  between  thermal  and  material  changes  occurring 
in  the  same  chemical  system. 

30  When  heat  is  imparted  to  a  gaseous  system  of  chemical 
substances,  a  portion  may  be  employed  in  increasing  the 
kinetic  energy  of  the  molecules,  i.e.  in  raising  the  temperature 
of  the  system ;  another  portion  may  be  employed  in  doing 
work  against  external  forces,  e.g.  in  causing  expansion  of  the 
system ;  and  another  portion  may  do  work  against  molecular 
and  atomic  forces,  and  so  produce  a  rearrangement  of  mole- 
cules, or  atoms,  i.e.  may  cause  chemical  changes  to  proceed 
within  the  system.  The  exact  manner  of  the  distribution  of 
the  energy  imparted  in  the  form  of  heat  will  vary  in  each  case. 
If  the  purely  chemical  part  were  separated  from  the  other  parts 
of  the  complete  change,  it  is  evident  that  the  thermal  value 
of  this  part  would  be  a  constant  quantity  only  under  constant 
physical  conditions.  Thus  the  difference  between  the  energy 
of  the  system  2H2+  O2  and  that  of  the  system  2H2O  (both  in 
grams)  at  ordinary  temperatures,  say  at  15°,  is  measured  by 
136,800  thermal  units;  but  if  the  initial  system  is  at  200° 
and  the  final  system  is  at  15°  the  difference  will  be  only 
116,500  units1 ;  assuming  that  the  total  loss  of  energy  to  the 
system  during  the  change  is  measured  in  each  case  by  the 
quantity  of  heat  produced.  Indeed  in  some  cases  change 
of  temperature  may  reverse  a  process  both  chemically  and 
thermally  without  altering  the  nature  or  the  masses  of  the 
reacting  substances;  thus 

at  ordinary  temperatures  2H2O  +  2C12  =  4HC1  +  O2 (0 

but  at  about  200°  4HC1  +  O2  =  2H2O  +  2C12  (2) ; 

if  reaction  (i)  is  expanded  thermally  it  becomes 

[2H2OAq,  2CPAq]  =  4|y/,  Cl,  Aq]  -  2  [H\  Q,  Aq]  =  20,400  units  : 
if  reaction  (2)  is  treated  in  the  same  way  we  have 

foffCt,  02]  =  2[#2,  0]-4[fft  C/]  =  28,500  units  (at  200°). 
If  the   reaction    occurs  between  bodies  in  solution,  the 
quantity  of  heat  which  is  produced   or   disappears   will  be 
dependent  on  the  temperature,  and  in  determining  the  thermal 
value  of  the  chemical  change  it  will  be  necessary  to  determine 

1  For  the  method  of  calculation,  see  The  Elements  of  Thermal  Chemistry,  par.  57. 

1 8— 2 


2/6  THERMAL   METHODS.  [BOOK  I. 

the  specific  heat  of  a  solution  of  each  of  the  reacting  bodies 
and  of  each  of  the  products  of  the  reaction1.  Heat  may  also 
be  produced  or  disappear  in  changes  of  volume,  or  changes  in 
the  states  of  aggregation,  of  the  reacting  bodies;  thus  any 
comparisons  or  contrasts  instituted  between  hydrochloric, 
hydrobromic,  and  hydriodic,  acid  from  a  consideration  of 
these  numbers, 

[//,  C7]  =  22,000;  [//,  Br]=  8,440;  [//,  I]=  -6,050 
must  be  accepted  with  great  reserve,  because  at  ordinary  tem- 
peratures chlorine  is  a  gas,  bromine  a  liquid,  and  iodine  a 
solid  ;   the   reactions   formulated    are  not,  therefore,  strictly 
comparable. 

131  There  is  another  point  to  be  noticed  in  analysing  the 
thermal  changes  which  accompany  chemical  processes,  viz., 
that  the  ordinary  notation  usually  represents  a  chemical 
change  as  a  much  simpler  phenomenon  than  it  really  is.  Most 
chemical  reactions  are  accomplished  only  by  employing  'an 
excess,'  sometimes  a  large  excess,  of  one  or  more  of  the  react- 
ing substances:  thus  the  equation 

AgCl  +  HI  (grams)  =  AgI  +  HCl 

would  more  nearly  express  the  distribution  of  the  masses  of 
the  reacting  bodies  if  it  were  written 


Potilitzin  has  investigated  this  subject  of  the  relations  be- 

tween the  thermal  value  of  a  change  and  the  masses  of  the 

changing  substances2.  The  heat  of  formation  of  a  metallic  chlo- 

ride is  greater  as  a  rule  than  that  of  the  corresponding  bromide, 

[MBr,  C/]  =  [M,  C/]  -  [M,  Sr]  >o. 

Again  it  is  generally  true  that 

[MBr,  HCl]  =  [M,  Cl}  +  [H,  Br\  -  [M,  Br\  -  [H,  Cl~\<o; 
e.g.[AgBr,//C/]=  -6,900:  [KBr,^C/]=  -3,250;  [NaBr,  HCl}=  -  1,600. 
Therefore,   it   would    appear   probable   that   chlorine   should 
decompose   metallic    bromides,   but    that    hydrochloric   acid 
should  not  react  with  these  salts. 

But  Potilitzin's  experiments  shew  that  the  reaction 


See  The  Elements  of  Thermal  Chemistry,  par.  55. 

See  abstract  in  Ber.  14.  2044;  and  15.  918;  also  16.  3051 


CH.  IV.  §§  1  3  I  ,  I  32]    THERMAL  AND  CHEMICAL  CHANGES.      277 

proceeds  at  275  —  300°  when  MCI  and  Br  are  employed  in 
equivalent  quantities,  (M  =  K,  Na,  or  Ag),  and  also  that  when 
MBr  and  Cl  react  in  equivalent  quantities  the  whole  of  the 
bromine  is  not  replaced  by  the  chlorine. 

By  increasing  the  amount  of  bromine,  relatively  to  MCI, 
in  the  reaction  above  formulated,  more  MBr  is  produced  until 
a  limit  is  reached  whereat  equilibrium  is  established.  This 
equilibrium  is  not  overthrown  even  by  increasing  the  mass  of 
bromine,  raising  the  temperature,  and  prolonging  the  time  of 
action. 

132  I  think  the  position  has  now  been  clearly  established  that 
the  thermal  value  of  a  chemical  change,  even  of  a  simple 
reaction  between  gaseous  substances,  really  represents  the 
sum  of  various  changes  some  of  which  have  a  positive  and 
others  a  negative  value.  Assuming  that  in  any  case  it  is 
possible  to  separate  the  gain  or  loss  of  energy,  measured 
thermally,  during  a  definite  chemical  reaction,  into  a  portion 
representing  physical  changes  and  another  portion  repre- 
senting purely  chemical  changes,  it  is  nevertheless  generally 
the  case  that  the  latter  portion  of  the  total  energy-change 
must  itself  be  analysed  before  an  accurate  and  precise  appli- 
cation of  the  thermal  value  can  be  made  ;  that  is  if  the  appli- 
cation is  to  proceed  on  the  lines  of  the  molecular  and  atomic 
theory.  For,  assuming  that  we  have  made  due  allowance  for 
the  influence  of  the  masses  of  the  reacting  substances  and 
for  the  possible  formation  and  decomposition  of  molecular 
groups  during  the  reaction,  there  yet  remains  the  important 
consideration  that  heat  is  produced  or  disappears  not  only 
in  the  formation  or  the  decomposition  of  compounds,  but  also 
in  reactions  of  decomposition  or  formation  of  elements,  which 
take  part  in  the  chemical  process. 

Let  us  analyse  a  comparatively  simple  reaction  ; 


When  this  is  expanded  thermally  we  have 

[2H2O,  2C/2]=4[#,  Cl~\+[O,  O]-2  [H2,  O]-  2  [C/,  Ct\. 
That  is  to  say,  heat  is  used  in  separating  each  chlorine  mole- 
cule into  atoms,  and  heat  is  produced  in  the  union  of  each 
pair  of  oxygen  atoms  to  form  a  molecule. 


2/8  THERMAL   METHODS.  [BOOK  I. 

Let  us  take  an  apparently  more  simple  instance 
[H*,  C12]  =  44,000  units. 

Remembering  the  fundamental  distinction  between  atoms 
and  molecules,  and  moreover  bearing  in  mind  the  fact  that 
the  molecules  of  hydrogen  and  chlorine  are  both  diatomic,  we 
may  expand  this  equation  thus 

[H2,  Clz]  =  2  [H,  CI]  -  [H,  H]  -  [Cl,  a]  =  44,000. 

But  we  do  not  know  the  true  thermal  value  of  any  one  of 
the  three  parts  of  this  reaction  ;  when  therefore  we  write 
[H2,  Cl2]  =  44,000,  we  use  a  short  way  of  expressing  the 
fact  that  when  2  grams  of  gaseous  hydrogen  combine  with 
71  grams  of  gaseous  chlorine  to  produce  73  grams  of  gaseous 
hydrochloric  acid,  at  ordinary  temperatures,  44,000  gram-units 
of  heat  are  produced. 

As  long  as  thermal  measurements  are  regarded  in  this 
way  they  convey  precise  and  important  information.  But  we 
want  something  more  than  this;  we  desire  to  have  some  light 
thrown  on  the  rationale  of  chemical  changes.  Now  our  most 
far-reaching  conceptions  in  chemistry  are  based  on  the  dis- 
tinction implied  in  the  terms  atom  and  molecule ;  until  then 
this  distinction  is  practically  recognised  in  thermal  chemistry, 
we  cannot  expect  great  advances  to  be  made  in  applying 
the  mass  of  data  already  accumulated  to  questions  of  the 
mechanism  of  chemical  change. 

133  In  the  Introduction  to  volume  I.  of  his  Essai  de  mecanique 
chimique,  Berthelot  lays  down  three  fundamental  principles  of 
thermal  chemistry  [p.  xxviii — xxix]. 

(1)  The  quantity  of  heat  produced  in  a  reaction  measures 
the  sum  of  the  physical  and  chemical  changes  which  occur  in 
that  reaction. 

(2)  The  total  thermal  value  of  a  reaction  is  dependent  only 
on  the  initial  and  final  states  of  the  changing  system. 

(3)  Every  chemical  change  accomplished  without  addition 
of  energy  from  without  tends  to  the  formation  of  that  body 
or  system  of  bodies  the  production  of  which  is  accompanied 
by  the  development  of  the  maximum  quantity  of  heat. 

The  first  and  second  principles  have  already  been  illus- 
trated and  discussed.  The  third,  under  the  name  of  the  "  law 


CH.  IV.  §133]  LAW   OF   MAXIMUM    WORK.  279 

of  maximum  work  "  forms  the  basis  of  all  Berthelot's  thermo- 
chemical  generalisations.  It  is  stated  in  an  even  more  rigid 
form  as  the  theorem  of  the  necessity  of  reactions*,  "  Every 
chemical  change  which  can  be  accomplished  without  the  aid 
of  a  preliminary  action  or  the  addition  of  energy  from  with- 
out the  system  necessarily  occurs  if  it  is  accompanied  by 
disengagement  of  heat." 

This  so-called  law  of  maximum  work  may  be  shewn 
theoretically  to  be  untrue2;  but  even  supposing  it  were  true, 
I  think  that  if  the  fundamental  distinction  between  atom  and 
molecule  is  clearly  grasped  it  will  be  seen  that  Berthelot's 
statement  is  too  general  to  throw  much  light  on  chemical 
changes. 

Berthelot's  law  is  simply  a  crude  application  of  the  prin- 
ciple of  the  degradation  of  energy;  the  principle,  namely,  that 
energy  always  tends  to  run  down  from  a  more  available  to  a 
less  available  form.  Inasmuch  as  the  formation  of  a  chemical 
compound,  with  production  of  heat,  is  an  instance  of  such 
running  down  of  energy,  from  the  form  of  chemical  affinity 
to  that  of  heat,  it  follows  that  the  reversal  of  this  process  will 
require  the  expenditure  of  work.  But  the  law  of  maximum 
work  does  not  attempt  to  analyse  the  expression  chemical 
affinity.  Under  this  term  Berthelot  includes  actions  and 
reactions  of  different  kinds.  This  is  at  once  apparent  from 
the  statement  in  the  Essai*  that  the  first  fundamental  principle 
of  thermal  chemistry,  viz. — "  the  quantity  of  heat  produced  in 
a  reaction  measures  the  sum  of  the  physical  and  chemical 
changes  which  occur  in  that  reaction  " — furnishes  the  measure 
of  chemical  affinities4. 

Berthelot's  work  is  saturated  with  the  conceptions  of  the 
molecular  theory :  but,  by  some  fatal  perverseness,  he  refuses 
to  apply  this  theory  to  chemical  phenomena.  While  recog- 
nising the  existence  of  molecules  and  building  his  generalisa- 
tions on  a  molecular  foundation,  he  refuses  to  accept  the 

1  loc.  dt.;  Introduction,  p.  xxix.,  also  2.  422. 

2  See  Book  n.  Chap.  n.  par.  191. 

3  Introduction,  p.  xxviii. 

4  '  Ce  principe  fournit  la  mesnre  dcs  ajfinites  chimiqucs.'' 


280  THERMAL   METHODS.  [BOOK  I. 

conception  of  atom,  or  rather  he  hopelessly  confuses  it  with 
that  of  equivalent.  The  molecule  is  for  him  a  definite  and 
definable  portion  of  matter,  the  parts  of  the  molecule  are  only 
numbers. 

If  by  chemical  affinity  is  meant  an  action  and  reaction 
between  atoms,  then  the  principle  already  quoted  certainly 
does  not  afford  a  measure  of  this  affinity. 

Berthelot's  law,  then, — assuming  its  truth — appears  to  be 
a  definite  statement  applicable  to  chemical  reactions;  but 
more  precise  investigation  shews  that  the  application  is  only 
possible  when  '  chemical '  is  used  in  a  vague  way  as  including 
much  that  is  usually  called  '  physical.' 

The  principle  of  the  degradation  of  energy  is  a  highly 
generalised  statement  applicable  to  certain  cycles  of  change; 
Berthelot  attempts  to  apply  it  to  parts  of  such  cycles,  forget- 
ting that  what  is  true  of  the  whole  is  not  necessarily  true  of 
the  parts. 

Thirty  years  ago  Thomsen1  generalised  the  relations  be- 
tween chemical  action  and  thermal  change  in  the  statement, 
"Every  simple  or  complex  reaction  of  a  purely  chemical  kind 
is  accompanied  by  production  of  heat." 

If  by  a  reaction  'of  a  purely  chemical  kind'  is  meant  the 
combination  of  atoms  to  form  molecules,  no  objection  can  be 
made  to  this  statement ;  we  recognise  its  importance  and 
universality,  as  we  recognise  the  same  qualities  in  such  state- 
ments as  '  all  men  are  mortal,'  or  '  no  white  men  are  black.' 
But  we  may  doubt  its  utility.  Thomsen  explains2  that 
'reactions  of  a  purely  chemical  kind'  are  those  which  proceed 
without  addition  of  energy  from  sources  external  to  the 
system,  and  consist  only  of  the  strivings  of  atoms  towards 
more  stable  equilibrium3.  On  the  other  hand  a  chemical 
system  may  be  raised  to  a  temperature  such  that  its  consti- 
tuents are  no  longer  stable,  and  reactions  may  then  occur 
with  expenditure  of  external  energy ;  but  these  changes 

1  See  Thermochemische  Unterstichungen,  1.  12 — 16. 

2  loc.  cit.  1.  1 6. 

3  "Der  chemische  Process  ist  rein  chemischer  Natur,  wenn  er  ohne  Aufwand 
fremder   Energie  verlauft,  und  nur  durch   das   Streben  der  Atome  nach  mehr 
stabilen  Gleichgewichtslagen  zu  Stande  kommt." 


CH.  IV.  §133]  LAW   OF   MAXIMUM    WORK.  28l 

do  not  depend  solely  on  mutual  atomic  attractions.  But 
actions  '  of  a  purely  chemical  kind '  never  occur  except  as 
parts  of  cycles  of  reactions  which  include  changes  that  do  not 
consist  'solely  of  the  strivings  of  atoms  towards  more  stable 
equilibrium.'  Hydrogen  and  oxygen  do  not  combine  to  form 
water,  neither  do  chlorine  and  hydrogen  combine  to  form 
hydrochloric  acid,  without  the  addition  of  energy  from  ex- 
ternal sources. 

If  the  statements  quoted  from  Thomsen  or  Berthelot  are 
ever  true,  they  are  true  only  when  an  arbitrary  separation  is 
made  of  chemical  changes  into  two  parts,  and  one  of  these 
parts  is  alone  called  chemical.  Every  chemical  change,  how- 
ever simple,  consists  of  at  least  two  parts,  the  first  of  which  is 
the  necessary  antecedent  of  the  second ;  the  law  of  maximum 
work  ignores  this  duality,  or,  it  might  be  more  accurate  to 
say,  the  law  assumes  that  the  second  part  of  a  chemical  pro- 
cess can  occur  without  the  first.  Every  process  of  chemical 
change  may  be  compared  to  the  flight  of  a  stone  from,  and 
its  return  to,  the  surface  of  the  earth.  During  the  first  part  of 
this  process  there  is  a  continual  transference  of  kinetic  energy 
from  the  moving  stone  to  the  surrounding  medium,  and 
during  the  second  part  there  is  a  continual  transference  from 
the  medium  to  the  stone,  until  the  stone  comes  to  rest  when 
its  energy  becomes  a  part  of  the  total  energy  of  the  system, 
earth  +  stone.  If  the  final  resting-place  of  the  stone  is  nearer 
the  centre  of  the  earth  than  the  spot  from  which  it  was  pro- 
jected on  its  upward  flight,  then  the  stone  contains  less  energy, 
relatively  to  surrounding  systems,  at  the  close  of  the  trans- 
action than  at  the  beginning.  On  the  other  hand,  if  the 
starting-point  is  nearer  the  earth's  centre  than  the  final  point 
of  rest,  then  the  transaction  has  resulted  in  gain  of  energy  to 
the  stone.  In  both  cases  the  second  part  of  the  transaction, 
that  which  occurs  between  the  turning-point  and  the  final 
resting-point  of  the  stone,  is  attended  with  loss  of  energy  to 
the  stone;  but  this  second  part  does  not  represent  the  com- 
plete transaction.  The  law  of  maximum  work  if  applicable 
at  all  is  applicable  only  to  the  second  part.  And  moreover 
this  law  ignores  the  fact  that  the  stone  (or  chemical  system) 


282  THERMAL   METHODS.  [BOOK  I. 

does  not  leave  its  initial  point  of  rest  of  its  own  accord;  the 
law  assumes  that  no  work  need  be  done,  no  energy  expended, 
in  the  passage  of  the  stone  (or  system)  from  its  original  posi- 
tion to  that  at  which  the  energy-relations  between  it  and 
surrounding  systems  come  within  the  cognisance  of  the 
law. 

134  An  attempt  has  been  made  by  Thomsen  to  measure  the 
thermal  values  of  the  first  parts,  i.e.  separation  of  molecules 
into  atoms,  of  certain  changes  which  result  in  the  production 
of  hydrocarbons.  Attention  has  been  already1  drawn  to  this 
investigation.  An  account  of  Thomsen's  argument  by  which 
he  arrives  at  a  certain  thermal  value  for  each  of  the  four 
'bonds'  of  the  atom  of  carbon  is  given  in  The  Elements  of 
Thermal  Oumistry  (pars.  73 — 75).  I  will  not  reproduce  that 
account  here,  but  rather  give  a  brief  statement  of  another  and 
later  argument  by  which  Thomsen  has  arrived  at  certain 
conclusions  regarding  the  thermal  values  of  the  '  bonds '  of 
the  atom  of  carbon. 

Thomsen2  assumes  (i)  that  the  four  'bonds'  or  'affinities' 
of  an  atom  of  carbon  are  of  equal  value,  at  least  as  regards 
combination  with  atoms  of  hydrogen,  (2)  that  all  the  hydrogen 
atoms  in  the  molecule  of  a  hydrocarbon  are  bound  to  the 
carbon  atom  with  equal  vigour,  and  (3)  that  carbon  atoms  may 
be  united  together  in  three  different  ways,  viz.  by  single, 
double,  or  treble,  linkings. 

The  heat  of  combustion  of  a  gaseous  hydrocarbon  mole- 
cule is  theoretically  divisible  into  two  parts,  (i)  the  heat  used 
in  separating  the  molecule  into  atoms  of  carbon  and  hydrogen, 
and  (2)  the  heat  produced  in  the  combination  of  these  atoms 
with  oxygen  to  form  carbon  dioxide  and  water. 

The  formula  CaHw  expresses  the  composition  of  paraffins. 
As  each  atom  of  carbon  has  four  bonds,  a  atoms  of  carbon 
have  4a  bonds ;  as  each  atom  of  hydrogen  has  one  bond  2b 
atoms  have  2b  bonds ;  but  every  carbon  atom  must  be  united 
to  another  carbon  atom  by  at  least  one  bond,  hence  the  total 
number  of  single  linkings  between  the  carbon  atoms  in  a 

1  Seeawfc,  chapter  II.  section  IV.  par.  85. 
a  Zeitschr.fiir physikal.  Chemie,  I.  369. 


CH.  IV.  §  134]      THERMAL  VALUE  OF  CARBON  BONDS.  283 

paraffin  molecule  CaH2A  is 


2 

Let  v  be  the  work  required  to  tear  asunder  two  singly 
linked  carbon  atoms,  then  the  work  required  to  tear  asunder 
all  the  singly  linked  carbon  atoms  in  a  paraffin  molecule  CaH2A 
is 

(2a-b}v (2). 

Let  r  be  the  work  required  to  tear  asunder  an  atom  of 
hydrogen  from  an  atom  of  carbon  to  which  it  is  linked  in  the 
molecule  CaHu,  then  the  work  required  to  tear  asunder  all 
the  hydrogen  atoms  in  the  molecule  is 

2*>- (3). 

Hence  the  work  required  to  isolate  all  the  atoms  com- 
posing the  molecule  CaH2i  is 

(2a-b)v  +  2br (4). 

Let/£  be  the  heat  of  combustion  of  an  isolated  gaseous 
carbon  atom,  and  let  fhz  be  the  heat  of  combustion  of  two 
isolated  gaseous  hydrogen  atoms,  then  the  heat  of  combustion 
of  the  isolated  atoms  obtained  by  tearing  asunder  the  mole- 
cule CaUnb  will  be 

afc+bfh, (5). 

And  the  difference  between  (4)  and  (5)  will  express  the 
heat  of  combustion  at  constant  volume  of  the  gaseous  mole- 
cule CaHw; 

The  heat  of  combustion  of  the  gaseous  molecule  C0HW  at 
constant  pressure  is  found  by  taking  into  account  the  thermal 
change  accompanying  the  change  of  volume  from  C,,HM  to 
«CO2+  £H2O;  the  expression  is 

f.  CaH2j  (const,  press.)  =  a  (fc  —  2v)  +  b  (fh%  —  2r+v  +  290)  +  580. . . (7). 

As  this  equation  holds  good  for  all  paraffins,  and  as  the 
expressions  in  brackets  are  the  same  for  all,  fc  —  2v  may  be 
put  as=;r,  and  fh^  —  2r  +  v  +  290  as=j;  thus  we  get  the 
simpler  form 

/.QjHjA  (const,  press. )  =  <w+4y  + 580 (8). 


284  THERMAL   METHODS.  [BOOK  I. 

Thomsen  then  finds  probable  values  for  x  and  y  from  the 
following  heats  of  combustion  at  constant  pressure  of  five 
paraffins  :  — 


[  =  C4Hlrt]  =  687,i9o        C(CH3)4  [  =  C5H12]  =  847,iio. 
From  these  data,  ten  values  tor  x  andy  are  found,  and  from 
these  the  following  most  probable  values  are  deduced  by  the 
method  of  least  squares:  — 

x=  106,170        7  =  52,530. 

The  heats  of  combustion  of  the  five  paraffins  given  above 
calculated  with  these  values  of  x  and  y  closely  agree  with  the 
observed  values;  the  largest  difference  is  720  units  in  the  case 
ofC4H10. 

But  when  the  observed  heats  of  combustion  of  four  defines 
(CaHw  where  a  =  b}  are  compared  with  the  values  calculated 
by  the  use  of  the  above  values  for  x  and  y,  it  is  found  that  the 
observed  are  always  much  greater  than  the  calculated  num- 
bers. The  following  data  give  the  differences  in  question:  — 

C2H4...  15,370        C4H8...  15,240        C6H12...  32,570. 
C3H6...  16,060        C5H10...i5,55o. 

In  the  molecule  C6H12  there  are  two  double  linkings 
between  carbon  atoms,  and  in  each  of  the  other  molecules 
there  is  one  double  linking;  therefore  the  mean  increase  of 
the  observed  over  the  calculated  heat  of  combustion  is  15,465 
units  for  each  double  linking. 

Thomsen  then  develops  a  formula  for  calculating  the  heat 
of  combustion  of  a  gaseous  olefine  in  a  way  similar  to  that 
already  sketched,  but  taking  account  of  the  existence  of 
'  double  linkings  '  in  the  olefine  molecules  :  applying  this 
formula  he  arrives  at  the  conclusion  that 

2v-u2=  15,465  .................................  (9), 

where  v  means,  as  before,  the  work  required  to  tear  asunder 
two  singly  linked  gaseous  carbon  atoms,  and  u  =  the  work 
required  to  tear  asunder  two  doubly  linked  carbon  atoms. 

Thomsen  then  turns  to  the  acetylenes  (CttHw  where 
&  =  a—i),  and  by  similar  reasoning  to  that  applied  to  the 


CH.  IV.  §  134]      THERMAL  VALUE  OF  CARBON  BONDS.  285 

paraffins  and  defines  he  concludes  that 


(10), 

where  v  has  the  same  meaning  as  before,  and  w  represents  the 
work  required  to  tear  asunder  two  trebly  linked  carbon  atoms. 
These  results  may  be  stated  in  various  ways.  If  we 
regard  a  double  link  between  carbon  atoms  as  two  several 
linkings,  and  a  treble  as  three  several  linkings,  then 

u  +  7732  =  v,  and  w  +  1  4640  =  v. 

Thomsen's  results  are  thus  equivalent  to  asserting  that  the 
quantity  of  heat  produced  in  forming  the  hypothetical  group 
=  C  —  C  =  from  gaseous  isolated  carbon  atoms  is  7732  units 
greater  than  half  the  quantity  of  heat  produced  in  forming  the 
hypothetical  group  =  C  =  C  =  from  carbon  atoms,  and  is  14640 
units  greater  than  one-third  of  the  quantity  of  heat  produced 
in  forming  the  hypothetical  group  —  C  =  C  —  from  atoms  of 
carbon.  Or,  let  the  heat  produced  in  forming  =  C  =  C  =  from 

I  I 

—  C  —    and   —  C  —    be   x   units,    then  the  heat  produced    in 

I  i 

forming  =  C  —  C=  from  the  same  carbon  atoms  is  -  +  7732 

units  ;  and  let  the  heat  produced  in  forming  -  C  =  C  -  from 

I  I 

-  C  —  and  —  C  —  be  y  units,  then  the  heat  produced  in  form- 

I  | 

ing  =  C  —  C  =  from  the  same  materials  is  -  +  14640  units. 

Thomsen's  values  represent  differences;  in  this  paper  he 
does  not  attempt  to  find  the  actual  thermal  value  of  either  a 
single,  a  double,  or  a  treble,  linking  between  carbon  atoms. 

If  the  combination  of  a  pair  of  carbon  atoms  by  a  double 
link  is  regarded  as  occurring  in  two  parts  each  bond  having 
its  own  thermal  value,  then  Thomsen's  numbers  assert  that 
each  half  of  this  process  is  accompanied  by  the  production  of 
rather  less  heat  than  half  of  that  produced  when  two  carbon 
atoms  combine  by  a  single  bond. 

If  we  admit  the  justness  of  Thomsen's  conclusions  we  shall 
be  forced  to  acknowledge  that  the  bonds  of  the  carbon  atom 
are  of  unequal  value;  but  one  of  the  assumptions  on  which 


286  THERMAL   METHODS.  [BOOK  I. 

Thomsen  has  based  his  argument  is  that  the  bonds  in  question 
are  equal  in  value.  In  one  case  however  value  here  means 
chemical  value  and  in  the  other  it  means  thermal  value.  Both 
terms,  value  and  bond,  are  misleading.  Instead  of  the  fre- 
quently used  expression,  '  in  the  molecule  CH4  all  the  bonds 
of  the  carbon  atom  are  of  equal  value/  it  would  be  much 
better  to  say,  'in  the  molecule  CH4  each  hydrogen  atom  is 
related  to  the  carbon  atom  and  to  the  rest  of  the  molecule  in 
the  same  way  as  every  other  hydrogen  atom.' 

It  should  be  noted  that  the  conclusions  arrived  at  by 
Thomsen  are  applicable  only  to  hydrocarbons,  and  that  they 
are  based  on  but  scanty  data. 

If,  as  Thomsen's  results  assert,  the  thermal  value  of  a 
carbon  bond  depends  on  whether  that  bond  is  satisfied  by  the 
bond  of  another  carbon  atom  or  by  that  of  a  hydrogen  atom, 
it  is  almost  certain  that  the  thermal  value  of  the  carbon  bond 
will  vary  according  as  it  is  satisfied  by  the  bond  of  an  oxygen, 
a  sulphur,  or  a  chlorine,  &c.  atom ;  and  if  this  is  so,  then  in 
all  probability  the  thermal  value  of  each  bond  of  the  atom  of 
oxygen,  sulphur,  &c.,  will  vary  with  the  nature  of  the  other 
atoms  with  which  the  atom  of  oxygen  or  sulphur  is  combined. 
The  affinity  of  atoms  for  atoms  cannot  be  measured  by  the 
thermal  values  of  the  atomic  bonds.  Indeed  these  bonds  are 
wholly  imaginary  existences ;  they  are  protean  and  for  ever 
escape  one's  grasp ;  whether  the  conception  we  try  to  form 
of  them  be  purely  chemical  or  partly  chemical  and  partly 
thermal,  it  is  at  the  best  but  a  blurred  and  wavering  image 
which  comes  between  us  and  reality. 

135  A  few  generalisations  have  been  established  regarding 
the  connexion  between  the  structure  and  the  boiling  points 
of  carbon  compounds.  Thus  the  difference  between  the 
boiling  points  of  two  consecutive  members  of  an  homologous 
series  of  carbon  compounds  is  frequently  about  19° :  but  the 
numbers  actually  obtained  shew  that  variations  in  the  boiling 
points  are  connected  with  variations  other  than  those  of  mole- 
cular weight.  Goldstein1  attempts  to  shew  that  the  proportion 

1  Ber.  12.  689:    also  abstract  of  paper  in  Russian,  C.  S.  Journal  Abstracts 
for  1882,  374. 


CH.  IV.  §135]  BOILING   POINTS.  287 

between  the  numbers  of  hydrogen  and  carbon  atoms,  besides 
the  total  number  of  these  atoms,  influences  the  boiling  points 
of  the  members  of  an  homologous  series.  Hydrocarbons  of 
analogous  constitution  must  be  compared,  i.e.  normal  hydro- 
carbons must  be  compared  with  normal, 

e.g.  CH3-CH2-CH2-CH3  with  CH3-CH2-CH2-CH2-CH3; 
or  iso-hydrocarbons  must  be  compared  with  iso-,  e.  g. 
CH(CH3)2-CH2-CH3with  CH(CH3)2-CH2-CH2-CH3; 

nor  can  the  differences  between  the  boiling  points  of  normal 
hydrocarbons  be  compared  with  the  differences  between  the 
boiling  points  of  iso-compounds. 

Goldstein  investigates  the  change  of  boiling  point  in  the 
series  of  normal  paraffins,  i.e.  hydrocarbons  of  the  form 
CH3-(CH2),-CH3[orCH3-CHR'-CHJ.  He  gives  the 
formula 

B.P.  =  b.p.  +  (i9  +  ^<L 

where  B.  P.  =  boiling  point  required,  b.  p.  =  boiling  point  of 
the  paraffin  containing  CH2  less  than  that  whose  B.  P.  is  re- 
quired, and  n  =  number  of  atoms  of  carbon  in  the  molecule  of 
the  paraffin  whose  b.  p.  is  known.  Thus,  the  boiling  point  of 
C5H12  (i.e.  CH3  (CH2)3CH3)  is  39°'O;  required  the  boiling  point 
ofC6H14(i-e.CH3(CH2)4CH3). 


=  39+19+12-66 

=  7o°-66  B.  P.  observed  =  7o°-6. 

Goldstein  calculated  the  B.P.  of  normal  heptane  (C7H16) 
to  be  98°'65  ;  shortly  after  this,  the  paraffin  was  obtained  in 
quantity  by  Thorpe,  and  the  boiling  point  was  found  to  be 

980'5- 

The  same  formula  appears  to  hold  good  for  determining 
the  difference  between  the  boiling  points  of  any  two  consecutive 
iso-paraffins  belonging  to  the  form  CH  (CH3)8—  (CH8)X  —  CH3. 


288  THERMAL   METHODS.  [BOOK  I. 

Thus, 

B.P.     Difference. 


If  this  is  so,  it  follows  that  the  difference  between  the 
boiling  point  of  a  normal  paraffin  and  its  corresponding  iso- 
paraffin  (of  this  form)  must  be  the  same  whatever  be  the 
molecular  weight  of  the  two  isomerides.  Experiment,  so  far 
as  it  has  gone,  seems  to  confirm  this  result  ;  thus, 

TJ.         ,  Difference  between  B.P.  of  normal 

and  iso-paraffin. 

C5H12  8"-S 

C6H14  8°-6 

C7H16  8°-5 

."'*  v;  We  have  very  little  precise  knowledge  regarding  the 
T-i  bpiling  points  of  isomeric  hydrocarbons.  From  the  data 
~w~*  accumulated  it  has  been  concluded,  that,  of  two  or  more 

isfpmeric  hydrocarbons,  that  one  has  the  lowest  boiling  point 
••-.    tibfe   molecule  of  which  is  characterised    by  containing   the 

greatest  number  of  '  side  chains  n.     Thus 

Pentane  (CBH12).  B.P. 

;...    ./<«)  normal:—  CH3(CH2)3-CH3  39° 

"*-     "1®  isopropyl-methylmethane  :  —  CH2-  CH(CH3)2-  CH3  3O°'5 

(c)  tetramethylmethane  :—  C(CH3)4  9°'5 

Hexane  (C6H14). 

(a)  normal  :—  CH3(CH2)4CH3  70°-$ 

(£)  isopropyl-ethylmethane  :—  CH2  -  CH(CH3)2  -  C2H5  62° 

(c)  di-isopropyl  :—  CH(CH3)2-CH(CH3)2  58° 

(d)  trimethyl-ethylmethane  :—  C(CH3)3(C2H5)  43°—  48° 

The  replacement  of  one  or  more  atoms  in  a  molecule  by 
another  atom  or  other  atoms  is  attended  with  a  change  of 
boiling  point.  The  data  accumulated  point  to  the  existence 
of  definite  relations  between  the  boiling  points  of  the  com- 
pounds and  the  nature  and  relative  positions  in  the  molecules 
of  the  substituted  and  substituting  atoms.  Thus  the  change 
from  a  hydrocarbon  to  an  alcohol  by  substitution  of  OH  for 
H  is  accompanied  in  many  cases  by  a  rise  of  about  100°  in 
the  boiling  point  ;  the  change  from  a  monohydric  to  a  dihydric 
1  For  data  see  Naumann,  loc.  dt.  pp.  168  —  172. 


CH.IV.  §§135— 138]  SUMMARY.  289 

alcohol  is  also  attended  by  a  rise  of  B.  P.  amounting  to  about 
100° ;  the  substitution  of  a  bromine  atom  for  an  atom  of 
chlorine  in  chloroderivatives  of  hydrocarbons  is  accompanied 
by  a  rise  of  B.  P.  equal  to  about  23°,  and  the  value  of  the 
increase  is  nearly  constant  in  very  many  cases1. 

36  In  this  section  I  have  tried  to  trace  some  of  the  connexions 
between   the  results  of  thermal   measurements  of  chemical 
phenomena  and  certain  statical  aspects  of  these  phenomena. 
We  have  found  that  every  chemical  phenomenon  is  a  complex 
occurrence,  and   that    it   is  almost    impossible  fully   to  dis-r 
tinguish  those  portions  which  would  more  appropriately  be 
called  physical  from  those  which  are  undoubtedly  chemical. 
We  have  also  found  that  thermal  measurements,  being  essen- 
tially measurements  of  changes  of  energy,  are  intimately  coQr 
nected   with  problems   belonging   to  chemical   kinetics,  and 
that  until  we  know  something  of  chemical  affinity  we  are  nat 
in  a  position  fully  to  discuss  the  data  of  thermal  chemistry.  § 

5 
SECTION  II.     Optical  Methods. 

37  In  this  section  I  wish  to  give  some  account  of  the  attempts 
which  have  been  made  to  elucidate  the  relations  existing  b£ 
tween  the  composition  of  chemical  compounds  and  (i)  th'e 
refractive  powers,  (2)  the  power  of  rotating  a  ray  of  polarised 
light,  and   (3)   the  absorption-spectra,  of  these  compounds. 
The  subject  is  more  limited  than  that  considered  in  the  first 
section  of  the  present  chapter ;  it  belongs  more  completely 
than  thermal  chemistry  to  the  domain  of  chemical  statics, 
although  like  other  questions  in  chemical  science  it  presents 
aspects  which  are  essentially  kinetical. 

38  Let  a  ray  of  light  pass  from  air  into  a  liquid  medium 
denser  than  air ;  let  the  angle  of  incidence  =  i,  and  the  angle 

of  refraction  =  r ;    then    —. —  =  11  =  refractive   index  of   the 
sin  r 

medium. 

1  An  account  of  the  present  state  of  knowledge  regarding  the  connexions 
between  the  B.P.  and  constitution  of  carbon  compounds  will  be  found  in  a 
pamphlet  by  W.  Marckwald,  Uber  die  Bez^ehiingen  zwischen  dem  Siedepunkte 
mill  tier  Zusammcnsetzitng  chcmischer  Verbindungcn.  (Friedlander,  Berlin,  1888). 

M.C.  19 


290  OPTICAL   METHODS.  [BOOK  I. 

Let    the   light   employed    consist   only   of   light    of   one 
wave-length,  and  let  the  liquid  medium  consist  of  a  single 

definite  chemical  compound,  then  the  quantity  f— -j-J  was 

called  by  Gladstone  and  Dale1  the  specific  refractive  energy  of 
the  liquid  examined  (^=spec.  grav.  of  the  liquid  referred  to 
water  as  unity).  Landolt2  called  the  product  obtained  by 


multiplying          r-J  into  the  molecular  weight  of  the  liquid, 

i.e.  \      i    )  M,  the  refraction-equivalent  of  the  liquid  compound 
in  question. 

The  quantity  (    ^    )  was  said  by  Gladstone  and  Dale  to 


be  independent  of  temperature3. 

Objection  has  been  taken  to  the  use  of  this  purely  em- 
pirical formula  in  attempts  to  trace  connexions  between  the 
constitution  and  refractive  powers  of  compounds4.  The  formula 

f  ^  -  J  .  —j  for  finding  the  refraction-equivalent  of  a  compound 

was  deduced  from  the  general  principles  of  Clerk  Maxwell's 
electro-magnetic  theory  of  light  by  A.  Lorenz,  and  also  in- 

dependently  by    H.    Lorenz5.     The  formula    f-^-  -  \~j  , 

where  Ap  =  refractive  index  of  the  theoretical  ray  of  infinite 
wave-length,  was  deduced  by  the  use  of  a  method  given  by 
Cauchy,  and  was  supposed  to  give  results  practically  inde- 
pendent of  dispersion.  Other  formulae  have  been  proposed 
by  different  physicists.  Briihl6  has  recently  examined  all  the 
formulas  hitherto  proposed  for  calculating  the  refraction- 
equivalents  of  compounds  ;  he  concludes  that  no  formula 
gives  the  true  laws  of  dispersion,  and  that  none  of  them 
enables  us  to  determine  whether  a  limiting  value  independent 

Proc.  R.  S.  12.  448,  and  Phil.  Trans.  153.  317. 

Pogg.  Ann.  122.  545  ;  and  123.  595. 

See  Proc.  R.  S.  18.  49  ;  and  also  Phil.  Trans.  160.  9. 

See  especially  Wiedemann,  Ber.  15.  467.  . 

Wied.  Ann.  9.  641  ;  11.  70. 

Ber.  19.  2821  (references  are  here  given  to  many  other  memoirs). 


CH.  IV.  §§138  —  140]    MOLECULAR   REFRACTION.  2QI 

of  dispersion  does  or  does  not  exist  for  the  quotient  ^~    . 

Bruhl  states  that  the  influence  of  the  dispersion  of  different 
bodies  on  their  refractive  powers  has  not  been  satisfactorily 
deduced  from  any  optical  theory;  and  that  in  investigations 
into  the  connexions  between  the  refractive  powers  and  the 
chemical  constitution  of  compounds  the  influence  of  disper- 
sion must  be  neglected  if  it  cannot  be  eliminated  by  purely 
empirical  methods. 

Of  the  different  formulae  proposed,  Bruhl  prefers 


_ 

+  2 

because  it  gives  results  which  are  more  consistent  and  less 
influenced  by  changes  of  temperature  than  those  obtained  by 
any  of  the  other  formulae. 

139  In     1863    Gladstone   and    Dale1   concluded    that   'every 
liquid    has   a    specific    refractive    energy   composed    of    the 
specific  refractive  energies  of  its  component  elements,  modi- 
fied   by   the    manner   of  combination.'     Many   and    lengthy 
memoirs  have  been  published  on  this   subject   since    1863  > 
the   general    result   has   been    to   confirm   the   statement   of 
Gladstone  and  Dale,  and  at  the  same  time  to  trace  a  more 
precise    connexion    between    the   refraction-equivalent   of    a 
compound  and  the  manner  in  which  the  elements  of  that  com- 
pound are  combined.     One  of  the  fullest  and  most  important 
memoirs    is    that    published    in    1887    by   BriihP.     As   this 
investigation  includes  many  of  the  results  formerly  obtained 
I  propose  to  confine  myself  in  the  main  to  giving  an  account 
of  this   work.     Investigations   have  been   confined   hitherto 
chiefly  to  liquid  compounds  of  carbon. 

140  Let  us  follow  Bruhl  in  calling  the  product  of  the  specific 
refractive  energy  and  the  molecular  weight  of  a  compound 
the  molecular  refraction  (R),  and  the  product  of  the  specific 
refractive   energy    and   the    atomic    weight   of    an    element 

1  See  Phil.  Trans.  160.  9. 

2  Annaltii,   235.    i  ;    or  Ber.  19.    2746;    or  Zeitschr.  fiir  physikal.   Chemie, 
1.  307. 

I9—2 


2Q2  OPTICAL   METHODS.  [BOOK  I. 

the  atomic  refraction  (r).     And,  as   Briihl    does,  let    us   use 
the  following  formulae  for  determining  these  constants  :  — 
-  A   M  y  -  \     A 


where  M=  molecular  weight,  and  A  =  atomic  weight1. 

Assuming  that  the  molecular  refraction  of  a  compound  is 
the  sum  of  the  atomic  refractions  of  its  constituent  elements, 
and  that  the  refraction  of  each  atom  has  a  constant  value  in 
all  its  compounds,  we  may  express  the  molecular  refraction  (R) 
of  a  compound  of  carbon  hydrogen  and  oxygen,  CBH2mOp,  as 


where  (r)C,  (r)H,  and  (r)O  represent  the  atomic  refractions  of 
carbon,  hydrogen,  and  oxygen,  respectively. 

By  determining  the  differences  between  the  molecular 
refractions  of  members  of  an  homologous  series  of  carbon 
compounds,  values  are  obtained  for  what  may  be  called  the 
molecular  refraction  of  the  group  CH2;  by  determining  the 
differences  between  the  molecular  refractions  of  a  series  of 
compounds,  differing  by  2H,  values  are  obtained  for  the 
atomic  refraction  of  hydrogen  ;  and  by  deducting  the  value 
for  2H  from  that  for  CH2,  a  number  is  obtained  which  is 
taken  as  the  atomic  refraction  of  carbon.  By  similar  methods 
a  value  can  be  found  for  the  atomic  refraction  of  oxygen. 
The  molecular  refraction  of  any  compound  of  carbon  hydrogen 
and  oxygen  can  then  be  calculated,  on  the  assumption  that 
the  value  is  equal  to  the  sum  of  the  atomic  refractions  of  the 
constituent  elements,  and  compared  with  the  observed  value. 
141  The  calculated  values  for  (R)  do  not  agree  in  every  case 
with  the  observed  values.  Hence  the  molecular  refraction  of 
a  compound  is  probably  connected  with  the  arrangement, 
as  well  as  with  the  nature  and  number,  of  the  atoms  which 
compose  the  molecule  of  the  compound.  What  then  is  the 
nature  of  the  connexion  between  the  arrangement  of  the 
atoms  forming  a  molecule  and  the  refraction  of  that  molecule  ? 
Bruhl  thinks  that  the  present  data  warrant  general  con- 

1  Briihl  uses  light  with  the  wave-length  of  the  ray  C  ;  many  observers  determine 
/a  for  the  red  hydrogen  line  H«. 


CH.  IV.  §141]  MOLECULAR   REFRACTION.  2Q3 

elusions  only  regarding  compounds  of  carbon,  hydrogen,  and 
oxygen. 

The  paragraphs  devoted  to  isomerism  (par.  69  et  seg.}  con- 
tain data  which  shew  that  isomerism  may  be  connected  either 
with  changes  in  the  actual  valencies  of  the  atoms  forming  a 
molecule,  or  with  changes  in  the  distribution  of  the  interatomic 
reactions.  Thus,  the  formula  C3H8O  expresses  the  composition 
of  (i)  propylic  aldehyde,  (2)  acetone,  and  (3)  allylic  alcohol; 
assuming  the  correctness  of  the  structural  formulae  of  these 
three  compounds,  viz. 
mur  PH  r/°  (2)  H3C-C-CH3,  (3)  H2C-CH-CH2OH, 

(I)      ttgLx   -  C  tt2  —  l-N^TT   » 

o 

(i)  and  (2)  contain  each  a  trivalent  carbon  atom  and  a 
monovalent  oxygen  atom  in  direct  union,  and  also  a  pair 
of  tetravalent  carbon  atoms,  and  (3)  contains  two  trivalent 
carbon  atoms  neither  of  which  is  in  direct  union  with  oxygen, 
and  also  a  tetravalent  carbon  atom  in  direct  union  with 
an  atom  of  oxygen  which  is  divalent.  The  actual  valencies 
of  the  atoms  are  the  same  in  (i)  as  in  (2),  but  are  not  the  same 
in  (3)  as  in  (i)  or  (2);  the  distribution  of  some  of  the  inter- 
atomic reactions  varies  in  (i),  (2)  and  (3).  In  none  of  these 
cases  is  the  molecule  saturated,  i.e.  in  no  case  does  each 
polyvalent  atom  directly  interact  with  its  maximum  number  of 
monovalent  atoms  (see  ante,  par.  70).  These  examples  shew 
that  isomerism  occurring  in  unsaturated  molecules  may  be 
connected  either  with  changes  in  the  actual  valencies  of 
some  of  the  atoms  or  with  changes  in  the  distribution  of  the 
interatomic  reactions.  But  when  isomerism  occurs  in  saturated 
molecules  it  must  be  connected  with  changes  in  the  distri- 
bution of  the  interatomic  reactions  and  not  with  changes 
in  the  actual  valencies  of  the  atoms,  because  saturated  mole- 
cules are,  by  definition,  those  in  which  each  polyvalent  atom 
directly  interacts  with  its  maximum  number  of  monovalent 
atoms.  The  following  structural  formulae  for  different  propylic 
alcohols  (C4HBOH)  illustrate  this  kind  of  isomerism: — 

XCH3  /CH3 

H3C-CHs-CH2-CHoOH,     CH-CHaOH,     HO-C-CH3. 

\CH3  \CH3 


294  OPTICAL   METHODS.  [BOOK  I. 

That  kind  of  isomerism  which  is  exhibited  only  by 
unsaturated  molecules  and  is  connected  with  changes  in  the 
actual  valencies  of  the  atoms  is  called  by  Briihl  saturation- 
isomerism,  while  that  kind  of  isomerism  which  is  exhibited 
both  by  saturated  and  unsaturated  molecules  and  is  connected 
with  changes  in  the  distribution  of  the  interatomic  reactions 
unaccompanied  by  changes  of  valencies  is  called  by  Briihl 
position-isomerism. 

Briihl's  data  shew  that  different  saturation-isomerides  of 
the  general  form  C^H^O^  have  different  molecular  refractions, 
but  that  the  molecular  refraction  of  a  series  of  position- 
isomerides  of  the  general  form  CxHyOz  is  nearly  a  constant 
quantity. 

In  order  to  find  the  exact  influence  on  the  molecular 
refraction  of  a  compound  CxHyOz  of  changes  in  the  valencies 
of  the  carbon  and  oxygen  atoms,  Briihl  first  finds  values  for 
the  atomic  refraction  of  the  tetravalent  carbon  atom  and  the 
divalent  oxygen  atom  in  saturated  molecules.  The  difference 
between  (R)  for  each  pair  in  the  homologous  series  C«H2>(+2 
gives  a  value  for  (R)  CH2;  as  the  formula  CMH2K+2  can  be 
expressed  as  #CH2+H2,  the  same  data  allow  a  value  for 
(R)H2  to  be  found;  the  difference  between  (R)CH2  and 
(R)H2  gives  (r)C.  By  similar  methods  (r)  O  is  found. 

Taking  CIV  and  O"  to  represent  a  tetravalent  atom  of 
carbon  and  a  divalent  atom  of  oxygen,  respectively,  then 
Briihl's  data  lead  to  the  values  * 

(r)  CIV  =  2-48  ;    (r)  O"  =  I  -58  ;    (r)  H  =  i  "04. 

Values  of  (R)  are  then  calculated  for  unsaturated  com- 
pounds containing  a  pair  of  directly  interacting  trivalent 
carbon  atoms,  using  the  above  values  for  (r)  C  &c.,  and 
the  calculated  values  are  compared  with  those  obtained  by 
experiment. 

The  influence  on  (R)  of  the  change  from  a  pair  of  directly 
interacting  tetravalent  carbon  atoms  to  a  pair  of  directly  inter- 
acting trivalent  carbon  atoms  is  then  determined ;  Briihl's  data, 
given  for  about  20  compounds  of  the  general  form  C^H^,  C^H^O,, 

1  The  formula  (  -^ j .  -r  is  used,  and  /u  is  determined  for  the  line  C. 


CM.  IV.  §§  141,  142]    MOLECULAR   REFRACTION.  295 

and  Q-HyCl^XX,  shew  that  this  change  is  accompanied  by  an 
increase  in  (R)  amounting  to  about1  1*85.  Determinations 
of  (R)  for  seven  compounds2  each  containing  two  pairs  of 
directly  interacting  trivalent  carbon  atoms,  shew  a  mean 
increase  in  (R)  of  2  x  175. 

Bruhl  states  these  results  by  saying  that  the  mean  partial 
value  of  an  etJiylene  grouping  of  a  pair  of  carbon  atoms  in  the 
molecular  refraction  of  a  compound  of  the  form  C.trH>Or  is 
175.  The  phrase  ethylene  grouping  of  two  carbon  atoms  is 
used  because  ethylene,  H2C—  CH2,  is  the  simplest  compound 
containing  a  pair  of  directly  interacting  trivalent  carbon 
atoms. 

Bruhl  then  determines  (R)  for  various  ketones,  aldehydes, 
and  other  compounds  C«H2WO  containing  a  monovalent 
oxygen  atom  in  direct  union  with  an  atom  of  carbon,  or  it 
may  be  said  containing  a  carbonyl  group,  C  —  O,  and  by 
subtracting  (R)  C«H2M(=  #CH2),  he  obtains  the  mean  partial 
value  of  a  carbonyl  grouping  of  an  oxygen  and  a  carbon  atom 
in  the  molecular  refraction  of  a  compound  C^H^O,  ;  this  value 
is  found  to  be  76. 

These  conclusions  may  be  stated  thus  :  — 


/C  —  C^,    and    76    added   for    each    carbonyl    grouping, 


(R)  CxHy02=^  (r)  C+y  (r)  H  +  z  (r)  O, 

where   (r)  C  =  2*48,  (r)O=rs8,   and   (r)  H  =  1-04,  with    175 

added  for  each  pair  of  carbon  atoms  grouped  as  in  ethylene, 
\ 

<C-0. 

142        Let  us  now  consider  one  or  two  of  the  applications  which 
Briihl  makes  of  these  conclusions. 

Acetic  aldehyde  CH8CHO  is  easily  polymerised  to  par- 
aldehyde  C6H12O8.  The  change  is  probably  represented  by 
the  equation 

3H3C  -  CHO  =  H3C .  HC  -  O  -  CH  .  CH3. 

0-C-O 

/\ 
HCH3 

1  The  maximum  is  2-29,  and  the  minimum  i'59;  difference  =  7. 

2  Two  compounds  CjjH.jn-a  and  five  diallyl  compounds. 


296  OPTICAL   METHODS.  [BOOK  1. 

If  this  is  correct,  we  have  three  carbonyl  groupings  in 
3CH3 .  CHO,  and  no  carbonyl  groupings  in  C6H12O3]  therefore 
(R)C6H12O3  ought  to  be  equal  to  three  times  (R)CH8.  CHO  di- 
minished by  3  x  76  =  2-28.  The  observed  value  of  (R)CH3. CHO 
is  11-5,  and  (i  1-5  x  3)  -  2-28  =  32*22  ;  the  observed  value  of 
(R)CfiH1203  is  32-4- 

Amylene  C5H10  is  easily  polymerised  to  diamylene  C10H20 ; 
the  molecules  of  both  compounds  probably  contain  one  pair 
of  directly  interacting  trivalent  carbon  atoms,  or  one  ethylene 
grouping ;  if  this  is  so,  the  molecular  refraction  of  diamylene 
ought  to  be  equal  to  twice  that  of  amylene  diminished  by 
the  value  for  one  ethylene  grouping,  which  is  175.  The  ob- 
served values  of  (R)  are  these;  C5H10  =  24-64,  C10H20  =  47'i2  ; 
now  24-64  x  2  =  49*28,  and  49*28—  47'I2  =  2'i6  which  is  slightly 
greater  than  175.  Two  isomerides  of  diamylene  are  known, 
tetrahydroterpene  obtained  by  the  reaction  of  phosphonium 
iodide  with  turpentine,  and  cymhydrene  obtained  from 
camphor  by  reaction  with  iodine.  The  observed  molecular 
refractions  of  the  three  isomerides  (C10H20)  are  these  : — 

diamylene  47'i2        . 

tetrahydroterpene  46-02  '"  jlj""1 

„     ...dlff.  =  '22. 

cymhydrene  45 '80 

The  calculated  value  of  (R)C10H20  is  45-6,  if  (r)C  =  2-48 
and  (r)H=  ro4 ;  as  (R)  observed  is  nearly  equal  to  (R)  cal- 
culated in  the  cases  of  tetrahydroterpene  and  cymhydrene, 
and  is  greater  by  1-52  than  (R)  calculated  for  diamylene,  we 
should  conclude  that  diamylene  contains  one  ethylene  group- 
ing, and  that  the  other  isomerides  contain  only  tetravalent 
carbon  atoms.  The  study  of  the  three  hydrocarbons  so  far 
as  it  has  gone  confirms  this  conclusion. 

Both  the  isomerides  pentene  and  isoprene,  C5H8,  probably 
contain  a  pair  of  ethylene  groupings  ;  pinene,  C10H16>  probably 
contains  one  ethylene  grouping,  and  each  of  its  isomerides 
diisoprene  and  limonene  probably  contains  a  pair  of  ethylene 
groupings.  Assuming  these  statements  to  be  correct,  and 
comparing  the  observed  with  the  calculated  values  of  (R)  for 
these  five  hydrocarbons,  we  have  these  results  : — 


C1I.  IV.  §  142]  MOLECULAR    REFRACTION.  297 

(R) 
calcd.  observd.  diff. 

f  pentene,  two  ethylene  groupings     24*22        24-60         +-38 
6    8 1 isoprene,  two 24*22        24-62        +-40 

fpinene,        one 43'i9        43'66         +-47 

Ci0H](i<  diisoprene,  two 44'94        45'°4         +'io 

(limonene,    two 44'94        45'o6         +-12 

The  structural  formulae  of  the  different  hydrocarbons  C6H10, 
C^H^,  C5H8,  and  C10H16,  are  not  yet  fully  ascertained,  but  it 
is  very  probable  that  the  statements  made  by  Bru'hl  con- 
cerning the  number  of  ethylene  groupings  in  each  are  correct ; 
some  of  these  hydrocarbons  belong  to  the  class  of  open  chain 
compounds  and  others  to  the  closed  ring  group  ;  hence,  if  we 
may  judge  from  these  data,  the  closing  of  a  chain  of  carbon 
atoms,  or  the  opening  of  a  ring  of  the  same  atoms,  does  not 
affect  the  molecular  refraction  provided  there  is  no  change  in 
the  saturation-isomerism  of  the  molecules.  In  confirmation 
of  the  conclusion  that  molecular  refraction  is  not  directly 
connected  with  the  existence  of  closed  rings,  Briihl  tabulates 
the  molecular  refractions  of  24  benzene  compounds,  belonging 
to  many  different  classes  but  each  containing  a  single  benzene 
nucleus,  and  shews  that  the  mean  difference  between  the  ob- 
served and  the  calculated  values  of  (R)  is  +3  x  r8i  (max. 
diff.  =  3  x  2-17,  min.  diff.  =  3  x  1-58),  the  calculated  values 
being  arrived  at  by  using  (r)C  =  2-48,  (r)O  =  1*58,  (r)H  =  1-04. 
Hence  it  appears  that  the  six-carbon  benzene  nucleus  con- 
tains three  ethylene  groupings1. 

A  considerable  amount  of  evidence  is  certainly  brought 
forward  by  BrUhl  in  support  of  the  statement  that  "  position- 
isomerides  have  nearly  identical  molecular  refractions,  but 
saturation-isomerides  have  different  molecular  refractions... 
the  increase  in  molecular  refraction  being  nearly  propor- 
tional to  the  number  of  ethylene,  acetylene4,  and  carbonyl, 
groupings,  and  this  proportionality  being  more  exact  the 
smaller  is  the  dispersion  of  the  compounds." 

1  For  an  example  of  the  application  of  Briihl's  method  to  the  terpenes,  see 
Ber.  21.  145. 

-  A  pair  of  directly  interacting  divalent  carbon  atoms  is  called  by  Briihl  an 
acetylene  grouping  of  two  carbon  atoms  ;  acetylene  (IIC-CH)  being  the  simplest 
compound  in  which  such  a  grouping  occurs. 


298  OPTICAL   METHODS.  [llOOK  I. 

Briihl  then  formulates  the  fundamental  refraction-law  as 
follows : — 

"The  atomic  refraction  of  carbon  and  oxygen  is  not  in- 
variable, but  depends  upon  the  [actual  valencies  of  those 
atoms  in  different  molecules]1.  The  atomic  refraction  of  these 
elements  is  however  nearly  constant  provided  saturation  is 
unchanged,  and  in  such  cases  is  only  very  slightly  dependent 
on  the  configurations  of  the  atoms.  The  monovalent  elements 
exhibit  nearly  invariable  atomic  refractions." 

In  support  of  the  last  part  of  this  statement  Bruhl  shews 
that  the  atomic  refractions  of  hydrogen  and  chlorine  calculated 
from  direct  observations  very  closely  agree  with  the  values 
calculated  from  observations  made  on  compounds  of  these 
elements;  that  (R)  HC1  gas  =  (r)  H  +  (r)  Cl  (from  direct  ob- 
servations of  (r)  H  and  (r)  Cl);  and  lastly  that  (r)  H  and  (r)  Cl 
deduced  from  observations  on  liquid  carbon  compounds  are 
the  same  as  (r)  H  and  (r)  Cl  deduced  from  observations  on 
gaseous  carbon  compounds. 

Nasini2  has  made  determinations  of  (R)  for  various  carbon 
compounds  containing  sulphur,  and  has  deduced  two  values 
for  the  atomic  refraction  of  sulphur  according  as  the  atom 
directly  interacts  with  two  other  atoms  or  with  only  one. 
Wiedemann3  has  arrived  at  similar  results.  The  atomic  re- 
fraction of  sulphur  appears  to  vary  largely  in  compounds 
containing  both  oxygen  and  sulphur. 

143  It  should  be  noticed  that  the  conclusions  arrived  at  by 
Briihl  can  be  applied  at  present  only  to  such  compounds  of 
the  forms  C,  H,  and  Cx  H,  O,  as  do  not  exhibit  large  dis- 
persion. Nasini's  observations4  on  naphthalene  derivatives 
and  other  compounds  with  large  dispersive  power,  and  some 
of  the  experiments  of  Gladstone5  on  compounds  containing 
relatively  very  much  carbon,  shew  that  the  nature  of  the 
connexion  between  the  refractive  powers  and  the  compositions 
of  compounds  has  not  yet  been  fully  elucidated6. 

1  Briihl  uses  the  expression  'satisfaction  of  the  affinity'  (Befriedigung  der 
Affinitdt).  2  Ber,  15.  2878.  3  Wied.  Ann.  17.  577. 

4  Gaz.  14.  150;  15.  59;  17.  72. 

5  C.  S.  Journal  Trans,  for  1884,  241. 

6  Kanonnikow  (original  paper  in  Russian;  see  abstract  in  Ber.  16.  3047)  has 


CH.  IV.  §§  143,  144]  POLARISATION.  299 

144  If  a  ray  of  plane  polarised  light  is  passed  through  a  plate 
of  quartz  cut  at  right  angles  to  its  optical  axis,  the  position  of 
the  plane  of  polarisation  of  the  emergent  ray  does  not  coincide 
with  that  of  the  incident  ray ;  the  plane  has  been  rotated 
through  a  certain  angle,  called  the  angle  of  rotation.  If  the 
rotation  takes  place  in  the  same  direction  as  that  in  which 
the  hands  of  a  watch  appear  to  move  as  we  look  at  the  face, 
the  quartz  is  said  to  exhibit  dextrorotatory  power ;  this  is 
expressed  by  prefixing  -f  to  the  value  of  the  angle  of  rotation. 
If  the  rotation  takes  place  in  the  direction  opposite  to  that  in 
which  the  hands  of  a  watch  appear  to  move  as  we  look  at  the 
face,  the  quartz  is  said  to  exhibit  laevorotatory  power ;  this  is 
expressed  by  prefixing  —  to  the  value  of  the  angle  of  rotation. 

Optically  active  transparent  media  are  those  which  rotate 
the  plane  of  polarisation  of  a  ray  of  light  passed  through 
them;  they  are  divided  into  dextrorotatory  substances,  e.g. 
some  specimens  of  quartz,  sugar  in  aqueous  solution,  &c.,  and 
laevorotatory  substances,  e.g.  other  specimens  of  quartz,  tur- 
pentine, quinine  in  alcoholic  solution1,  &c. 

To  determine  the  amount  of  rotation  caused  by  any  sub- 
stance, it  is  necessary  to  have  an  instrument  wherein  a  ray  of 
light  may  be  polarised,  and  the  position  of  the  plane  deter- 

found  the  molecular  refractions  of  a  number  of  solid  carbon  compounds,  by 
dissolving  them  in  chemically  inactive  solvents  and  measuring  the  refractive 
indices  of  the  solutions,  the  values  of  the  indices  of  the  solvent  being  known. 
Kanonnikow  concludes  that  neither  the  degree  of  concentration  of  the  solution, 
nor  the  physical  condition  of  the  solid,  exerts  any  marked  effect  on  the  refractive 
power  of  the  dissolved  substance.  Conclusions  are  drawn  as  to  the  structural 
formulae  of  various  carbon  compounds ;  Bruhl's  generalisations,  on  the  whole,  are 
confirmed. 

The  same  chemist  (see  abstract  in  £er.  17.  ref.  157;  the  abstracts,  referate,  in 
the  Berichte  beginning  with  vol.  1 7  are  paged  separately  from  the  original  papers) 
has  attempted  to  determine  (r)  for  various  metals,  by  finding  (R)  for  various  salts 
of  carbon  acids  and  deducting  (R)  for  the  acids.  His  numbers  point  to  the 
conclusion  that  in  a  'group'  of  metals  (as  'group'  is  used  in  the  classification 
based  on  the  periodic  law)  (r)  increases  as  the  atomic  weights  of  the  metals 
increase.  Kanonnikow  also  tries  to  deduce  values  for  (R)  for  the  groups  NO3, 
SO4,  &c. ,  and  so  to  find  the  distribution  of  the  interatomic  actions  in  sulphates, 
nitrates,  &c.  (See  also  Bull.  Soc.  Chim.  41.  548.) 

1  For  details  concerning  polarised  light,  and  circular  polarisation  considered 
from  the  physical  stand-point,  see  Glazebrook's  Physical  Optics,  chaps,  xi. 
and  xiv. 


300  OPTICAL   METHODS.  [BOOK  I. 

mined  ;  the  polarised  ray  may  be  passed  through  a  known 
quantity  of  the  medium  under  examination  ;  and  finally  the 
position  of  the  plane  of  the  emergent  ray  may  be  deter- 
mined. Such  instruments,  known  as  polarimeters  or  polaristro- 
bometers,  are  described  in  detail  in  various  text-books1. 

Let  us  consider  a  liquid  carbon  compound,  say  C10H16. 
The  angle  of  rotation,  a,  depends  on  (i)  the  thickness  of  the 
layer  of  liquid  through  which  the  light  passes,  (2)  the  wave- 
length of  the  ray  of  light  employed,  and  in  most  cases 
(3)  the  temperature  at  which  the  observation  is  made.  The 
first  of  these  conditions  will  be  determined  if  we  know  the 
length  of  the  column  of  liquid  employed,  and  the  second 
is  rendered  definite  by  making  use  of  monochromatic  light. 

Let  /=  length  of  column  of  liquid  in  decimetres,  ^=spec. 
grav.  of  liquid  referred  to  water  at  4°,  and  a  =  angle  of  rotation 
of  plane  of  polarisation  of  light  of  given  wave-length2;  then 

[a]=  specific  rotatory  power  of  the  liquid,  for  the  given  ray,=  j—  j. 

That  is  to  say,  the  specific  rotatory  power  of  an  optically 
active  substance  is  the  angle  through  which  the  plane  of 
polarisation  of  a  given  ray  is  rotated  by  passing  through  a 
column  i  decimetre  long  of  a  liquid  containing  I  gram  of  the 
substance  in  I  cubic  centimetre. 

For  chemical  purposes  it  is  sometimes  better  to  adopt 
the  definition  of  molecular  rotatory  power  \iri\  suggested  by 

Krecke3,  viz. 

m      a 
100'  l.d* 

where  m  =  molecular  weight:  m  is  divided  by  100  to  obviate 
the  use  of  inconveniently  large  numbers. 
We  have  then 


r    n      m       a 

and  M=—  -7^. 

1  See   especially   Armstrong  and   Groves,   Organic  Chemistry,  569    et  scq.  ; 
and  also  Watts's  Dictionary,  3rd  Supplt.  1198—1207. 

2  It  is  customary  to  indicate  the  light  employed  by  placing  a  letter  below  the 
bracket  ;  thus  [a]D  means  spec,  rotatory  power  for  light  of  wave-length  D. 

3  J.fiir  prakt.  Chemie  (2).  .5.  12. 


CH.  IV.  §  144]         SPECIFIC   ROTATORY    POWER.  3O1 

If  the  substance  to  be  examined  is  a  solid,  it  must  be 
dissolved  in  an  optically  inactive  menstruum.  In  such  a  case, 
/=  length  in  decimetres  of  column  of  solution  employed,  p  = 
grams  of  optically  active  substance  in  100  grams  of  solution 
(i.e.  gram-percentage  composition),  and  «f=spec.  grav.  of 
solution  referred  to  water  at  4°;  then/.  d=c  =  concentration, 
i.e.  grams  of  active  substance  in  100  c.c.  of  solution;  and, 
assuming  that  the  solvent  has  no  influence  on  the  rotatory 
power  of  the  dissolved  substance, 


As  the  value  of  [2]  generally  rises  as  temperature  rises1, 
thermometric  observations  must  be  made.  The  value  of  [3] 
also  varies  with  variations  in  (i)  the  nature,  and  (2)  the 
quantity,  of  the  inactive  solvent  employed  ;  the  preceding 
formula  therefore  gives  only  the  apparent  specific  rotatory 
power  of  the  solid  substance. 

That  [a]  varies  according  to  the  nature  of  the  solvent  is 
shewn  by  Hesse's  observations  on  turpentine  oil2; 

pure  turpentine  oil+alcohol  oil  +  benzene  oil  +  acetic  acid 

(CIOH,e)  (amount  of  solvent  varied  in  each  case  from  10  per  cent,  to  90  per  cent.) 


[a]B        37°'oi  ;    37°'035  to  38°'486  ;  37°'i94  to  39°'449  >  37°'i48  to  4o°'222. 
The  following  numbers3  illustrate  the  dependence  of  [x] 
on  the  amount  of  solvent  employed; 
Value  of  [a]0 

Aqueous  solution  of  maximum.  minimum.  Difference. 

Tartaric  acid  +    I4°'i8  +     3°'2o  io0-98 

Codeine  -  137°75  -iii0>5o  26°'25 

Quinine  -  i6g°-2$  -ii6°-o  53°'25 

Landolt  (loc.  cit.}  has  shewn  that  the  true  value  of  [a] 
for  a  solid  or  liquid  may  be  found  in  many  cases  from  a  num- 
ber of  observations  made  with  solutions  of  varying  concen- 
tration; the  more  concentrated  the  solution  the  more  nearly 

1  For  numbers  illustrative  of  this  in  the  case  of  aqueous  solutions  of  tartaric 
acid  see  Diet.  3rd  Supplt.  1  209. 

2  Hesse,  Annalen  176.  89  and  189  :  see  also  Landolt's  Handbook  of  the  Polari- 
scope  (English  translation),  54  —  94.    This  book  presents  a  view  of  the  whole  subject 
of  circular  polarisation,  chemically  considered.    See  also  Landolt,  Ber.  21.  191. 

8  Landolt,  loc.  cit, 


3O2  OPTICAL   METHODS.  [BOOK  I. 

does  the  value  found  for  [a]  approach  the  true  value,  i.e.  the 
more  nearly  does  the  observed,  agree  with  the  true,  specific 
rotatory  power.  It  is  better  to  use  several  solvents  and  make 
a  series  of  observations  with  each;  the  value  deduced  for  [a] 
is  generally  the  same  for  each  solvent. 

The  nature  and  extent  of  the  variations  in  [a]  caused  by 
varying  the  quantity  of  solvent  appear  to  differ  for  each 
optically  active  solid  substance1;  in  some  cases  the  relation  is 
very  complicated,  in  others  it  may  be  expressed  by  a  com- 
paratively simple  formula2. 

That  the  observed  and  calculated  values  of  [a]  agree 
closely,  provided  a  sufficient  number  of  observations  is  made, 
is  evident  from  these  results  (Landolt) : — 


[a]/>  calculated  from  observations  on  mixtures  with 

Active  substance.       [a]o  observ 

ed        (i)               (2) 

(3) 

(4)                (5)     max.diff. 

C2H5OH      CH3OH 

H20 

C6H6    CH3CO2H 

Dextrorotatory  "1 
ethyl  tartrate  J 

8°-27       8°'42 

8°  -09 

-             - 

-'22 

Dextrorotatory  }           0- 

1  4°  -87 

+  72 

turpentine     J 

Lsevorotatory    | 
turpentine       J 

36°-97          — 

- 

36°'97     36°-89 

-'12 

Laevorotatory    )        ,  0 

_.--_.:__             f        l61    '55 

i6o°-83          — 

i6i°-29 

—           — 

-72 

nicotine 

The  true  specific  rotatory  powers  of  camphor,  cane  sugar, 


Active  substance. 

Solvent. 

[a]D  for 
pure  substance. 

[a]0  for 
dilution. 

Difference. 

Isevorotatory  turpentine 

alcohol 

36°"97 

38°79 

+    I°'82 

dextrorotatory       ,, 

PJ 

I4°'I7 

i5°'35 

+   i°'i8 

lae  vorotatory  nicotine  

falcohol 
(water 

i6o°-83 

74°'i3 

-22°'24 

-87°-i6 

[alcohol 

8°-27 

io°-i9 

+     I°'92 

(water  8°'O9  28°-i2  +2o°-o3 

2  Thus,  for  solutions  of  turpentine  in  alcohol,  Landolt  gets  the  formula 

[a]D=360'974 +  -004816417  + ooo  [331^ 

where  q  —  percentage  of  inactive  solvent.  (For  more  details  see  Landolt,  loc. 
cit,  81 — 94.)  For  dry  inverted  sugar  Grubbe  (Ber.  18.  2207)  finds  the  following 
formula  when  f  varies  from  o°  to  30°;— 

[>]£=  ~  •23°'3°5  +  '30406  (/-  20)  +  -001654  (/  -  2o)2. 

For  a  fuller  treatment  of  the  methods  employed  for  finding  the  true  value  of 
[a]  from  observations  on  solutions,  see  Diet.  3rd  Supplt.  1 2 1 2 — 1213;  also  Landolt , 
Per.  21.  191. 


CH.  IV.  §§  144,  145]    SPECIFIC    ROTATORY   POWER.  303 

and  dextroglucose,  have  been  determined  by  Landolt,  Tollens, 
and  Schmitz1.  But  I  think  it  should  be  noted  that  the  obser- 
vations on  which  is  based  the  method  for  determining  [a] 
were  necessarily  made  with  solutions  of  liquid  compounds  in 
inactive  solvents,  whereas  in  the  cases  of  camphor  and  sugar 
we  have  to  deal  with  solutions  of  solid  substances  ;  it  is 
possible  that  the  value  of  [a]  for  liquid  camphor  may  be  diffe- 
rent from  that  for  solid  camphor2.  It  should  also  be  observed 
that  any  deductions  concerning  the  relations  between  specific 
rotatory  power  and  molecular  structure,  drawn  from  a  study 
of  liquid  compounds,  could  not  be  applied  in  a  precise  manner 
to  solid  compounds,  assuming  the  true  value  of  [a]  for  these 
compounds  to  be  known. 
145  In  attempting  to  trace  relations  between  the  specific  rota- 
tory power  and  the  composition  of  compounds,  we  must  dis- 
tinguish relationships  between  [a]  and  the  composition  of 
molecules  whose  empirical  formulae  at  least  are  known,  from 
those  between  the  same  constant  and  such  mixtures  of  mole- 
cules in  varying  proportions  as  are  presented  by  solutions  of 
varying  concentration. 

For  although  in  the  latter  cases  no  precise  conclusions  can 
be  drawn  regarding  the  relative  arrangements  of  the  atoms  in 
the  molecules,  yet  the  study  of  specific  rotatory  power  may 
help  to  throw  light  on  such  general  questions  as  the  action  of 
solvents,  the  distinction  between  chemical  and  physical  change, 
and  so  forth. 

Pribram3  has  determined  [a]  for  aqueous  solutions  of  cane 
sugar,  tartaric  acid,  and  nicotine,  with  the  result  that  [a]  does 
not  become  constant  even  in  very  dilute  solutions4.  Pribram 
thinks  that  this  result  is  more  in  keeping  with  the  hypothesis 

1  See  Landolt,   loc.    cit.  84—92:    Tollens,   and   Schmitz  in   Ber.  9.    1531: 
10.  1403  :  and  do.  1414. 

2  Biot  states  that  fused  liquid  tartaric  acid  is  markedly  dextrorotatory,  but  the 
solidified  acid  is  feebly  Isevorotary  (Diet.  3rd  Supplt.  1209).     Landolt's  value  of 
[a]  for  solid  camphor  is  55°'6  (see  Diet.,  loc.  «V. -374):   while  Gernez  obtained 
the  value  7O°'33  for  fused  camphor  (do.  do.  p.  1209). 

3  Ber.  20.  1840. 

4  The  most  dilute  solutions  used  were,  '222  p.ct.  for  cane  sugar,  '3471  p.ct. 
for  tartaric  acid,  and  '8826  p.ct.  for  nicotine. 


304  OPTICAL   METHODS.  [BOOK  I. 

that  the  solvent  brings  about  some  gradual  change  in  the 
configuration  of  the  atoms  forming  the  molecule  of  the  dis- 
solved compound,  than  with  either  of  the  other  hypotheses1 
that  have  been  suggested,  one  of  which  asserts  that  the  mole- 
cules of  the  solid  consist  of  aggregates  of  true  molecules,  and 
that  these  are  separated  by  the  solvent,  and  the  other  supposes 
that  the  solvent  forms  a  series  of  compounds  with  the  dissolved 
substance,  which  compounds  are  of  different  rotatory  powers 
and  vary  in  quantity  with  variations  in  the  relative  amounts 
of  the  solvent  and  the  dissolved  substance. 

146  All  known  compounds  which  possess  the  power  of  ro- 
tating the  plane  of  polarisation  of  a  ray  of  light  when  in 
the  liquid  state  or  in  solution  are  compounds  of  carbon : 
van't  Hoff2,  following  in  the  steps  of  Le  Bel3,  has  endeavoured 
to  trace  a  precise  connexion  between  the  molecular  structure 
of  these  compounds  and  their  rotatory  power.  The  hypo- 
thesis of  Le  Bel  and  van't  Hoff  connects  optical  activity  with 
the  presence  of  one  or  more  asymmetric  carbon  atoms  in  the 
molecule  of  the  optically  active  body.  The  definition  of 
an  asymmetric  carbon  atom  implies  the  conception  of  the 
arrangement  of  atoms  in  three  dimensions  in  space.  An 
atom  of  carbon  is  supposed  to  be  situated  at  the  centre  of 
a  regular  tetrahedron,  and  to  be  in  direct  union  with  four 
atoms  or  radicles  situated  at  the  four  summits  of  the  tetra- 
hedron ;  when  these  four  atoms  or  radicles  are  all  different, 
two  geometrically  different  forms  of  the  configuration  may 

Fig.  46.  Fig.  47. 


1  References  to  memoirs  in  which  these  hypotheses  are  discussed  will  be  found 
in  Pribram's  paper. 

2  La  Chimie  dans  FEspace;  and  more  particularly  in  a  pamphlet  published  in 
1887,  entitled  Dix  Annees  dans  fhistoire  d'une  Theorie. 

'  Bull.  Soc.  Chim.  22.  337;  23.  295. 


CH.  IV.  §146]      ASYMMETRIC   CARBON    ATOMS.  305 

exist.  These  two  forms  bear  to  each  other  the  relation  of  an 
object  to  its  image ;  neither  is  superposable  on  the  other 
(s.  figs.  46  and  47).  An  atom  of  carbon  related  in  this  way 
to  four  different  radicles  is  said  to  be  asymmetric,  because 
there  is  no  symmetry  in  the  configuration,  while  at  the  same 
time  a  plane  of  symmetry  arises  so  soon  as  two  of  the  four 
radicles  are  the  same. 

Any  compound  containing  an  asymmetric  carbon  atom 
may  exhibit  geometrical  isomerism  :  each  isomeride  will  differ 
from  the  other  in  rotatory  power,  and  if  the  isomerides  are 
crystallisable  they  will  assume  enantiomorphous  (non-super- 
posable)  forms.  Ammonium  malate,  for  instance,  crystallises 
in  two  enantiomorphous  forms,  as  represented  in  figs.  48  and 
49;  these  crystals  differ  exactly  in  the  same  way  as  the 


Fig.  48. 


Fig.  49- 


molecules  of  the  two  isomerides  are  supposed  to  differ.  Many 
other  optically  active  compounds  shew  differences  in  rotatory 
power  accompanied  by  the  power  of  crystallising  in  enantio- 
morphous forms1. 

We  should  expect  then  to  find  all  those  compounds  opti- 
cally active  the  molecules  of  which  contain  one  or  more 
asymmetric  carbon  atoms,  and  also  to  find  that  all  optically 
active  compounds  contain  asymmetric  carbon  atoms. 

So  far  as  investigation  has  gone,  the  molecule  of  every 
compound  which  exhibits  rotatory  power  contains  at  least 
one  carbon  atom  in  direct  union  with  four  different  radicles2. 
The  following  formulae,  in  which  the  asymmetric  carbon 

1  Van't  Hoffs  Dix  Anntes...  p.  30. 

2  For  details  of  individual  compounds  s.  van't  Hoff,  /.  c.  pp.  31 — 48. 

M.  C,  20 


306  OPTICAL   METHODS.  [BOOK  I. 

atoms  are  indicated  by  italics,  shew  the  composition  of  some 
commonly  occurring  optically  active  compounds  ; — 

OH  OH 
I        I 

Tartaricacid CO2H  — C— C— CO2H  ; 

i        i 
H      H 
H 
I 

Lactic  acid CH3  — C— CO2H; 

I 

OH 
H 
I 
Secondary  amylic  iodide  CH3  —  C  —  C3H7. 

I 

Investigation  has  also  shewn  that  those  derivatives  of 
optically  active  compounds  which  do  not  themselves  contain 
asymmetric  carbon  atoms  do  not  possess  rotatory  power;  in 
other  words,  a  change  of  structure  resulting  in  the  removal 
of  the  asymmetric  atoms  is  always  accompanied  by  loss  of 
optical  activity.  But  compounds  do  exist  which  certainly 
contain  asymmetric  carbon  atoms  and  yet  do  not  rotate  the 
plane  of  polarisation  of  a  ray  of  light.  Some  of  these  may 
be  resolved  into  two  isomerides  of  equal  and  opposite  rotatory 
powers,  e.g.  racemic  acid ;  others  cannot  be  resolved  into 
active  isomerides,  e.g.  mesotartaric  acid. 

Consider  the  formulae 

(RaRaRO  C .  C(R1R2R3)  and  (R6R5R4)  C .  C(R1R2R3), 
where  R^  &c.  represent  different  radicles  ;  the  first  formula 
shews  each  of  the  two  asymmetric  carbon  atoms  in  direct 
combination  with  the  same  radicles  [R^R^R,,,  and  (CR^R,,)], 
the  second  formula  shews  one  asymmetric  carbon  atom  di- 
rectly combined  with  the  radicles  RI}  R2,  R3,  and  (CR4R5R6), 
and  the  other  asymmetric  carbon  atom  in  direct  union  with 
the  radicles  R4,  R6,  R6  and  (CR^RJ.  The  first  formula 
represents  a  symmetrical  molecule,  the  second  an  tmsymme- 
trical  molecule. 

Let  us  now  advance  a  step  farther  and  compare  the 
structures  represented  by  the  formulae 

(R3R2R1)C.C(R1R2R3)   and   (R2R3Rt)  C.  CC 


CH.  IV.  §146]      HYPOTHESIS   OF   VAN'T    HOFF.  307 

Both  formulae  are  symmetrical,  but  the  structure  repre- 
sented by  one  is  the  reflection  or  image  of  that  represented 
by  the  other.  The  isomeride  represented  by  one  of  these 
formulae  ought  to  rotate  the  plane  of  polarisation  to  the  right, 
and  the  other  isomeride  ought  to  rotate  the  plane  an  equal 
amount  to  the  left.  A  mixture  or  compound  of  these  isome- 
rides  in  equal  molecular  proportions  would  be  optically  in- 
active, because  every  dextrorotatory  molecule  would  be 
opposed  by  a  laevorotatory  molecule.  But  such  a  mixture 
or  compound  would  be  resolvable  into  a  dextrorotatory  and 
a  laevorotatory  isomeride. 

Unsymmetrical  compounds  containing  asymmetric  carbon 
atoms  must  be  active,  or  if  inactive  they  must  be  resolvable 
each  into  two  isomerides  of  opposite  rotatory  powers. 

Inactive  compounds  which  are  resolvable  into  two  isome- 
rides of  equal  and  opposite  activities  are  said  in  the  language  of 
van't  Hoff's  hypothesis  to  be  inactive  by  external  compensation. 

Now  let  the  structure  represented  by  the  formula 


be  considered1.  Each  half  of  this  molecule  is  the  complement 
or  reflected  image  of  the  other  ;  one  half  will  neutralise  the 
optical  activity  of  the  other  half;  the  whole  will  be  inactive 
by  internal  compensation. 

A  compound  which  is  inactive  by  internal  compensation 
must  contain  at  least  two  asymmetric  carbon  atoms,  and  the 
formula  must  be  symmetrical.  The  hypothesis  asserts  the 
existence  of  such  inactive  compounds,  and  declares  that  they 
cannot  be  resolved  into  active  isomerides  because  their  in- 
activity is  the  result  of  the  atomic  configuration  of  their 
molecules,  and  is  not  produced  by  the  opposition  of  molecules 
of  dextrorotatory  power  to  an  equal  number  of  isomeric 
molecules  of  laevorotatory  power. 

The  hypothesis  of  van't  Hoff  divides  compounds  containing 
asymmetric  carbon  atoms  into  three  classes  :  — 

(i)  Those  which  are  optically  active:  such  compounds 
are  produced  in  pairs  consisting  of  a  dextrorotatory 

1  Models  of  the  different  structures  made  in  pasteboard  are  helpful. 

2O  —  2 


308  OPTICAL   METHODS.  [BOOK  I. 

and  a  laevorotatory  isomeride ;    they  are  either  sym- 
metrical or  unsymmetrical. 

(2)  Those  which  are  inactive  but  may  be  resolved  into 
two  isomerides  of  equal  and  opposite  rotatory  powers  ; 
they  are  inactive  by  external  compensation. 

(3)  Those  which  are  inactive  and   non-resolvable;   they 
are  inactive  by  internal  compensation. 

Van't  Hoff  (I.e.  pp.  54 — 55)  shews  that  an  unsymmetrical 
compound  containing  n  asymmetric  carbon  atoms  may  exist 
in  2"  optically  different  modifications,  and  that  a  symmetrical 
compound  containing  11  asymmetric  carbon  atoms  may  have 

|2*  active  isomerides,  and  |22  inactive  non-resolvable  isome- 
rides1. 

There  are  three  general  methods  for  separating  inactive 
resolvable  bodies  into  their  dextrorotatory  and  laevorotatory 
isomerides. 

In  the  first  method  advantage  is  taken  of  the  differences 
between  the  actions  of  some  minute  organisms  on  the  two 
active  isomerides.  For  instance,  when  penicillium  is  allowed 
to  act  on  a  dilute  solution  of  ammonium  racemate,  Isevorota- 
tory  tartrate  of  ammonium  is  found  in  the  liquid  after  a  time, 
the  isomeric  dextrorotatory  tartrate  being  destroyed  by  the 
action  of  the  organism. 

The  second  method  proceeds  by  treating  the  inactive  com- 
pound with  an  active  body  with  which  one  of  the  isomeric 
constituents  of  the  inactive  compound  combines  more  readily 
than  the  other.  For  instance,  crystals  of  laevorotatory  tartrate 
of  cinchonine,  and  a  solution  of  dextrorotatory  tartaric  acid, 
may  be  obtained  by  adding  the  proper  quantity  of  active 
cinchonine  to  a  solution  of  racemic  acid,  and  crystallising. 

The  third  method  consists  in  separating  the  inactive  body 
into  two  active  isomerides  by  crystallisation  at  a  definite 
temperature.  For  instance,  when  a  solution  of  racemic  acid 
is  neutralised  by  soda  and  another  equal  quantity  by  ammonia, 
and  the  solutions  are  mixed  and  evaporated  at  a  temperature 
a  little  below  28°,  crystals  both  of  dextrorotatory  and  laevoro- 

1  Many  applications  are  given  in  pp.  55 — 62  of  van't  Hoff's  Dix  Annces,  &c. 


CH.  IV.  §§  146,  147]      HYPOTHESIS   OF   VAN'T   HOFF.  309 

tatory  sodium-ammonium  tartrate  are  obtained1.  Van't  Hoff2 
has  shewn  that  the  change  from  sodium-ammonium  racemate 
to  the  two  tartrates  is  accomplished  by  heating  the  dry  salt 
with  water  in  the  ratio  NaNH4 .  H4C4O6 .  H2O:  sH2O  to  a  little 
under  27°;  and  that  the  change  from  the  two  tartrates  to 
the  racemate  (and  water)  is  effected  by  heating  the  dry 
mixture  to  a  little  above  27°.  The  changes  may  be  repre- 
sented thus  (the  racemate  crystallises  with  H2O  and  the  tar- 
trates with  4H2O) : 

2(NaNH4.H4C4O6.4H2O)^2(NaNH4.H4C4O6.H2O)  +  6H2O. 

Slight  variations  of  temperature  above  or  below  27°  deter- 
mine the  direction  in  which  the  change  occurs.  Some  other 
racemates  appear  to  undergo  change  to  tartrates  at  a  definite 
temperature2. 

The  change  of  inactive  racemates  to  the  active  tartrates 
and  vice  versa  is  closely  analogous  to  some  changes  which 
occur  among  inorganic  compounds ;  for  instance,  when  a 
mixture  of  the  sulphates  of  magnesium  and  sodium  in  mole- 
cular proportion  is  heated  a  little  above  21°  it  is  changed  to 
a  double  sulphate  and  water,  and  at  a  little  under  21°  the 
double  sulphate  is  resolved  into  the  two  single  sulphates : — 
MgS04 .  7H2O  +  Na8SO4  .  ioH2O  ^  MgNa2  (SO4)2 .  4H2O  +  I3H2O. 

The  process  of  resolution  by  heat  of  the  inactive  racemate 
is  also  very  analogous  to  the  physical  process  of  fusion ;  and 
as  one  speaks  of  the  fusion-point,  so  van't  Hoff  uses  the 
expression  transition-point  to  indicate  the  temperature  at 
which  the  chemico-physical  change  in  question  occurs8. 
47  The  hypothesis  of  van't  Hoff  and  Le  Bel  connects  the 
power  of  rotating  the  plane  of  polarisation  of  a  ray  of  light 
primarily  with  the  configuration  of  the  parts  of  molecules,  but 
it  points  to  the  formation  of  molecular  aggregates  without 
change  of  molecular  structure  as  a  cause  of  the  removal,  or 
rather  disappearance,  of  optical  activity.  Optical  activity 
appears  to  be  independent  of  the  nature  and  number  of  the 

1  For  examples  of  the  application  of  the  three  methods,  see  van't  Hoff,  /.  c. 
pp.  64-69. 

3  See  van't  Hoff,  /.  c.  p.  69. 

3  For  details,  see  van't  Hoff,  Journal fiir  physikal.  Chemie,  1.  165,  227. 


3IO  OPTICAL   METHODS.  [BOOK 

atoms  which  form  the  molecule  of  a  carbon  compound,  and  to 
be  connected  only  with  the  configuration  of  these  atoms.  We 
cannot  assign  a  definite  part  of  the  total  rotatory  power  of  a 
compound  molecule  to  each  of  the  atoms  or  even  groups  of 
atoms  which  form  the  molecule ;  nor  can  we  connect  the 
rotatory  power  with  changes  of  valency  or  with  changes  in 
the  distribution  of  the  atomic  interactions,  except  in  so  far  as 
these  are  concerned  in  changes  from  a  configuration  contain- 
ing asymmetric  carbon  atoms  to  another  configuration  which 
does  not  contain  such  atoms. 

The  specific  rotatory  powers  of  many  compounds  readily 
undergo  change  when  small  changes  occur  in  certain  physical 
conditions.  Some  active  bodies  become  inactive  by  heating, 
and  at  another  temperature  the  change  is  sometimes  reversed. 
The  value  of  [a]  of  a  solution  of  an  active  body  in  an  inactive 
solvent  is  dependent  on  the  nature  and  the  quantity  of  the 
solvent.  The  addition  of  one  inactive  solvent  to  the  solu- 
tion of  an  active  body  in  another  solvent  is  sometimes 
accompanied  by  a  great  change  in  the  rotatory  power  of  the 
liquid  ;  thus  about  one  half  of  the  alcohol  in  an  alcoholic 
solution  of  cinchonine  may  be  replaced  by  chloroform  without 
much  change  of  rotatory  power,  but  if  as  much  as  ^th  °f 
the  chloroform  in  a  solution  of  the  same  alkaloid  in  this 
solvent  is  replaced  by  alcohol  a  marked  change  in  rotatory 
power  occurs1.  Again,  the  rotatory  power  of  a  body  in  solu- 
tion sometimes  changes  on  keeping  until  a  constant  value  is 
attained;  thus  the  value  of  [a]  for  a  freshly  prepared  aqueous 
solution  of  milk  sugar  or  certain  glucoses  decreases  on  keep- 
ing, and  the  final  value  is  more  quickly  attained  by  boiling 
the  liquid2. 

This  readiness  to  change  shewn  by  the  rotatory  powers  of 
carbon  compounds  finds  some  explanation  in  van't  Hoff's 
hypothesis,  especially  in  the  development  of  it  made  by 
Wislicenus.  For  Wislicenus  shews3  that  besides  those  con- 
figurations which  are  conditioned  by  the  affinities  of  the 

1  Watts's  Diet.  3rd  Supplt.  1210. 

2  Land  oil's  Handbook  of  the  Polariscope,  p.  62. 

3  See  ante,  par.  94. 


CH.  IV.  §§  147,  148]      MAGNETIC  ROTATORY  POWER.  3!! 

atoms  of  a  molecule  containing  asymmetric  carbon  atoms,  other 
configurations  will  probably  exist  which  will  be  relatively 
unstable,  and  that  the  existence  and  number  of  these  will  be 
conditioned  by  the  action  of  heat  and  by  collisions  with  mole- 
cules of  other  kinds ;  as  these  unstable  forms  are  only  geome- 
trically different  from  the  stable  configurations  they  will  be 
optically  active,  but  their  rotatory  power  will  not  probably  be 
the  same  as  that  of  the  stable  form. 

Krecke1  has  endeavoured  to  generalise  the  relations  be- 
tween the  molecular  rotatory  powers*  [m]  of  certain  compounds 
and  of  their  active  derivatives ;  but  the  data  are  insufficient. 
148  A  large  number  of  measurements  of  the  rotatory  power 
of  compounds  when  under  magnetic  influence  has  been  made 
by  Perkin3.  The  liquid  compound  to  be  examined  was  placed 
in  a  glass  tube  the  ends  of  which  were  let  into  the  poles  of  a 
large  electromagnet;  the  tube  formed  part  of  a  polariscope. 
Sodium  light  was  employed. 

A  great  many  compounds  exhibit  optical  activity  under 
these  conditions. 

Perkin  measures  the  rotations  of  liquid  compounds  and 
refers  the  results  to  lengths  of  liquids  related  to  each  other  in 
the  same  proportion  as  the  molecular  weights  of  the  gases 
obtained  by  vapourising  these  liquids. 

The  molecular  rotation  of  water  is  taken  as  unity.  Let  r  = 
observed  rotation  of  a  specified  compound  and  r  =  rotation 
of  water;  let  Mw  =  molecular  weight  of  the  compound  and 
Mw  =  molecular  weight  of  water;  and  let  a?=spec.  grav.  of 
the  compound  and  ^'  =  spec.  grav.  of  water  [=  i];  then  mole- 

_, .      r .  Mw     r .  Mw 
cular  rotatory  power  (Mol.  R)  = 


r' .  Mw'  .d' 

1  J-  JUr  prakt.  Chemie,  (2).  5.  6.    See  also  Flavitsky,  Ber.  15.  5  ;  Th.  Thomsen, 
Ber.  13.    2168,    2264,  2269;   14.   29,    134,    203,  807,    1647;   and   against   him, 
Landolt,  Ber.  14.  296,  1048. 

2  See  ante,  p.  300. 

3  C.  S.  Journal,  Trans.  1884.  421 ;  1886.  777;  1887.  808. 


312  OPTICAL   METHODS.  [BOOK  I. 

About  150  compounds  were  examined,  the  observation  of 
r  being  repeated  five  to  ten  times  for  each  compound,  and  the 
spec.  grav.  of  each  being  carefully  determined. 

In  strictly  homologous  normal  carbon  compounds  each 
increment  of  CH2  produces  a  constant  increment  (i'O23)  in 
molecular  rotatory  power.  But  when  the  addition  of  CH2  is 
accompanied  by  a  change  in  the  distribution  of  the  atomic 
interactions  the  change  of  Mol.  R.  is  not  constant  ;  for  in- 
stance, the  change  from  a  normal  paraffin  CHs.?zCH2.  CH3  to 
the  next  higher  isoparaffin  CH(CH3)2.  «CH2.  CH3  produces 
an  increase  in  Mol.  R.  equal  to  1-023  +  '105;  in  the  change 
from  a  normal  acid  to  the  next  higher  iso-acid  of  the  same 
series,  CH.2  has  a  different  value;  and  so  on.  When  chlorine  is 
substituted  for  hydrogen  in  a  hydrocarbon  the  molecular 
rotatory  power  is  increased,  but  each  chlorine  atom  has  a 
different  value  from  the  others. 

These  results  indicate  that  the  molecular  rotatory  power 
of  a  compound  is  not  the  sum  of  certain  constant  values 
assignable  to  each  atom  or  atomic  group,  but  that  it  depends 
on  the  arrangement  of  the  atoms  which  form  the  molecule. 
This  result  is  confirmed  by  the  outcome  of  attempts  to  assign 
values  to  the  atomic  rotatory  powers  of  oxygen  and  carbon. 
The  atomic  rotatory  power  of  hydrogen  may  be  deduced 
thus:  — 


(1)  Mol.  R.  of  C0H2n  +  2=Mol.  R. 

but  Mol.  R.  of  #CH2  =  «  1-023. 

The  value  thus  deduced  for  At.  R.  of  H  is  -254. 

(2)  Mol.  R.  of  QH^  =  Mol<  R  Qf  CmH2m  +  i  . 

then  'Mol.  R.  of  CnH2n  +  2-  Mol.  R.  of  CmHta  +  1 

=  At.  R.  of  H,  if  n  =  m; 
[e  g       Mol.  R.  ofC6H14  _  3-323=Mol  R  of  C3H7  . 

but      Mol.  R.  of  C3H8  =  3-577,  .'.  At.  R.  of  H  =  "254]. 

The  value  thus  deduced  for  At.  R.  of  H  is  "254. 

The  difference  between  -508  (At.  R.  of  H  =  -254)  and  1-023 
(Mol.  R  for  CHa  in  normal  homologous  series)  gives  the  num- 


CH.  IV.  §  148]      MAGNETIC   ROTATORY    POWER.  313 

her  '515  as  the  atomic  rotatory  power  of  carbon  in  normal 
homologous  series.  Similar  methods  are  applied  to  the  data 
for  oxygen  compounds,  and  the  results  are  these; — 

Oxygen  in  alcoholic  OH   At.  R.  =  'i94, 

Oxygen  in  carboxylic  OH     „      =-137, 

Oxygen  in  carboxylic  CO     „      ='261. 

When  these  values  are  applied  to  calculate  Mol.  R.  for  series 
different  from  those  which  furnished  the  data,  numbers  are 
obtained  which  do  not  agree  with  the  observed  numbers. 

Nor  can  a  constant  value  be  found  for  the  atomic  rotatory 
power  of  chlorine;  the  value  varies  according  to  the  series  of 
compounds  considered,  according  as  one  or  two  hydrogen 
atoms  are  replaced  by  one  or  two  chlorine  atoms,  according 
as  the  hydrogen  replaced  is  in  one  part  of  the  molecule  or 
in  another  part,  and  so  on. 

The  general  conclusion  is  that  change  of  molecular  rota- 
tory power  of  carbon  compounds  under  magnetic  influence  is 
intimately  connected  with  changes  in  molecular  structure,  so 
that  any  cause  which  alters  this  structure  also  alters  the 
rotatory  power. 

Perkin  attempts  to  use  determinations  of  Mol.  R.  for  various 
compounds  formed  by  the  action  of  water  on  other  compounds 
for  throwing  light  on  the  question  whether  these  compounds 
are  hydrates,  i.e.  compounds  of  water,  or  compounds  of  oxygen 
and  hydrogen  with  other  elements. 

In  all  measurements  of  Mol.  R.  the  molecular  rotatory 
power  of  water  under  the  magnetic  influence  is  taken  as 
unity;  if  therefore  a  compound  is  formed  by  addition  of  water 
to  another,  Mol.  R.  for  the  new  compound  might  be  expected 
to  be  equal  to  that  for  the  original  compound  plus  one  for 
each  molecule  of  water  added ;  if  the  observed  Mol.  R.  is  less 
than  Mol.  R.  thus  calculated,  the  difference  may  be  explained 
by  supposing  that  the  formation  of  the  new  compound  has 
involved  a  rearrangement  of  the  atoms  of  the  reacting  mole- 
cules. Here  are  a  few  examples  of  the  application  of  this 
method : — 


314  OPTICAL   METHODS.  [BOOK  I. 

HCO2H  .  H2O     Mol.  R.  observed  =  2  '666     Mol.  R.  HCO2H  +  i 

"   =2-671 
CH3C02H.H20  „  „  3-554  „       CH3C02H  +  i 


CH3CH2CO2H  .  H2O  „  „  4-512  „      CH3CH2CO2H 

+  1=4-462. 

H2S04  „  „  2-315 

H2S04.    H2O  „  „  3-188  =  Mol.  R.  H2SO4+  -873 

H2SO4.2H20  „  „  4-113=       „       H2SO4.H,0 

+  •925 

H2SO4.3H2O  „  „  5-064=       „       H2SO4.2H2O 

+  •951- 

Perkin  considers  that  the  bodies  formed  by  adding 
water  to  formic  acetic  and  propionic  acids  are  either  hydrates 
of  these  acids,  or  only  mixtures;  but  that  a  compound  of  sul- 
phur oxygen  and  hydrogen  [perhaps  SO(OH)J,  and  not  a 
hydrate  of  sulphuric  acid,  is  produced  when  sulphuric  acid 
and  water  react  in  the  ratio  H2SO4:  H2O.  The  difference 
between  Mol.  R.  for  some  organic  anhydrides  and  Mol.  R.  for 
the  corresponding  acids  averages  about  74;  in  other  words, 
the  combination  of  a  molecule  of  water  with  an  anhydride  to 
form  an  acid  raises  Mol.  R.  by  about  74;  hence,  Perkin 
argues,  when  H2O  is  added  to  H2SO4  the  change  which  occurs 
is  so  far  analogous  to  that  of  the  conversion  of  an  anhydride 
into  an  acid  that  it  cannot  be  regarded  as  a  simple  hydration 
of  sulphuric  acid. 

The  following  data  lead  to  the  conclusion  that  chloral 
hydrate  is  not  a  compound  of  chloral  and  water,  but  that  the 
reaction  between  these  compounds  involves  a  rearrangement 
of  some  of  the  atoms  of  the  reacting  bodies:  — 

Mol.  R.  of  CC13.  CHO  liquid  =  6'59i 

Mean  Mol.  R.  of  liquid  CC13  .  CHO  .  H2O  =  7-037 

Increase  in  Mol.  R.  for  combination  of  H2O  =  '446. 

149  Researches  on  the  relations  between  the  composition  and 
the  absorption-spectra  of  carbon  compounds  have  been  con- 
ducted by  Hartley1.  From  the  results  thus  obtained,  Hartley 
concludes,  that  the  normal  alcohols  CnH2n+1  .  OH  are  remark  - 

1  Phil.  Trans.  170.  257.  See  also  C.  S.  Journal's™.™,  for  1881.  153  et  seq. 
See  also  report  of  the  B.A.  committee  ^gn  Spectrum  Analysis;  Brit.  Ass.  Reports 
for  1880.  258  et  seq. 


CH.  IV.  §  149]  ABSORPTION-SPECTRA.  315 

ably  transparent  to  the  ultra-violet  rays — methylic  alcohol 
transmits  all  rays  up  to  wave-length  2000,  but  octylic  alcohol 
transmits  nothing  beyond  3464;  that  a  normal  acid  of  the 
CnH2im  CO2H  series  always  exhibits  a  greater  absorption  of 
the  more  refrangible  rays  of  the  ultra-violet  spectrum  than  the 
normal  alcohol  with  the  same  number  of  carbon  atoms; 
and  that  in  both  alcohols  and  acids  addition  of  CH2  is  accom- 
panied by  increased  absorption. 

From  an  examination  of  the  absorption-spectra  of  very 
many  carbon  compounds,  Hartley  concludes,  that  absorption- 
bands  are  never  present  in  the  ultra-violet  part  of  the  spec- 
trum obtained  by  passing  light  through  a  compound  in  the 
molecule  of  which  the  carbon  atoms  are  arranged  in  an  'open 
chain',  but  that  such  bands  are  present  in  the  absorption- 
spectra  of  all  benzene  derivatives.  Inasmuch,  however,  as 
benzene  hexachloride  C6H6C16  is  very  transparent,  and  exhi- 
bits no  bands,  it  would  appear  that  the  mere  closing  of  the 
chain  of  carbon  atoms  is  not  the  sole  condition  necessary  for 
the  production  of  absorption-bands.  Hartley  thinks  that  each 
carbon  atom  must  be  in  direct  union  with  at  least  three  other 
carbon  atoms. 

This  supposition  is  in  accordance  with  the  observation 
that  solutions  of  naphthalene,  anthracene,  and  phenanthrene, 
in  transparent  media,  shew  absorption-bands,  similar  to,  but 
lower  in  refrangibility  than,  the  benzene  bands ;  and  that 
these  solutions  likewise  exhibit  much  more  intense  absorption 
than  benzene. 

Terpenes  (C10H16)  and  camphor  (C]0HJ6O)  exhibit  more 
intense  absorption  than  compounds  of  the  paraffinoid  group, 
but  no  bands  appear  in  the  spectra  of  the  light  transmitted 
by  these  compounds ;  hence  their  molecular  structure  appears 
to  be  related  on  the  one  hand  to  the  paraffinoid  and  on  the 
other  hand  to  the  benzenoid  group  of  compounds. 

By  taking  advantage  of  the  differences  in  the  character 
of  the  absorption  exhibited  by  different  compounds — e.g.  the 
character  of  the  absorption-spectrum  of  cymene  is  very  dif- 
ferent from  that  of  the  terpenes — it  is  possible  to  detect 
minute  quantities  of  certain  compounds  in  presence  of  large 


316  OPTICAL   METHODS.  [BOOK  I. 

quantities  of  others,  and  also  broadly  to  classify  carbon 
compounds  into  groups.  Further,  by  taking  advantage  of 
the  differences  in  the  positions  of  the  bands  in  the  spectra  of 
the  light  transmitted  by  isomeric  compounds,  it  will  be 
possible,  when  sufficient  data  have  been  obtained,  to  de- 
termine the  class  to  which  this  or  that  isomeride  belongs. 
Moreover,  the  gathering  together  of  this  data  will  doubtless 
be  the  means  of  gaining  much  precise  knowledge  regarding 
the  relations  between  the  molecular  structure  and  the  actinic 
properties  of  compounds1.  For  the  experiments  of  Hartley  * 
tend  to  the  conclusion  that  although  greater  or  less  absorp- 
tion is  connected  with  molecular  vibrations,  yet  the  special 
selective  absorption  characteristic  of  benzenoid  compounds  is 
rather  to  be  connected  with  atomic  vibrations.  These  ex- 
periments also  shew  that  the  mean  rate  of  vibration  of  the 
rays  absorbed  by  molecules  of  naphthalene  and  anthracene 
is  less  than  that  of  the  rays  absorbed  by  benzene  molecules, 
and  hence,  remembering  the  similarity  of  the  character  of  the 
absorptions  in  these  three  cases,  it  is  concluded  that  the 
amplitudes  of  the  vibrations  of  the  naphthalene  and  anthra- 
cene molecules  are  greater,  and  the  rates  of  vibration  are 
slower,  than  those  of  the  benzene  molecules.  Hence  it  would 
follow  that  the  atomic  vibrations  which  probably  give  rise  to 
the  observed  selective  absorption  are  closely  dependent  on 
the  vibrations  of  the  molecules  as  wholes. 

Now  if  a  connexion  between  the  vibrations  of  molecules 
and  the  vibrations  of  parts  of  these  molecules  is  established, 
and  if  this  connexion  is  elucidated  by  precise  data,  we  shall 
certainly  have  made  an  important  advance  in  solving  the  fun- 
damental problem  of  chemistry,  which  is  to  trace  the  relations 
between  the  composition  and  the  properties  of  bodies. 

A  further  step  in  this  direction  has  been  made  by  Abney 
and  Festing3,  who  have  mapped  the  absorption  which  occurs 
in  the  infra-red  region  of  the  spectrum,  and  have  thus  been 

1  For  the  application  of  his  general  conclusions  to  essential  oils,  quinoline, 
hydrocyanic  and  cyanuric  acids,  &c.,  see  Hartley,  C.  S.  Journal  Trans,  for  1880. 
676 ;  do.  for  1882.  45 ;  and  Chem.  News,  40.  269. 

5  C.  S.  Journal  Trans,  for  1881.  165—167. 

3  Proc.  R.  S.  31.  416,  and  Phil.  Trans,  for  1881.  887. 


CH.IV.  §§  149,  150]      MOLECULAR   VOLUMES.  317 

able  to  shew  that  there  is  a  definite  connexion  between  the 
nature  of  the  atomic  groups  in  the  molecules  of  many  carbon- 
compounds,  and  the  vibrations  of  the  rays  stopped  by  these 
compounds1. 

SECTION  III.    Methods  based  on  determinations  of  the  molecular 
volumes  of  compounds'2. 

150  The  quotient  obtained  by  dividing  the  formula-weight  by 
the  specific  gravity  of  a  compound  (referred  to  water  at  4°)  is 
generally  called  the  specific  volume  of  that  compound.  The 
term  specific  volume,  however,  evidently  expresses  the  relative 
volume  of  unit  weight  of  the  substance.  The  quotient  in 
question  is  sometimes  called  the  molecular  volume  of  the  com- 
pound formulated.  This  expression  strictly  interpreted  im- 
plies that  the  formula-weight  is  identical  with  the  molecular 
weight,  and  that  the  specific  gravity  and  formula-weight  are 

1  Kriiss  and  Oeconomides  (Ber.  16.  2051),  and  Kriiss  (Ber.  18.   1426,  2586), 
have  traced  some  connexion  between  the  shifting  of  absorption  towards  or  away 
from  the  less  refrangible  part  of  the  spectrum  and  the  substitution  of  hydrogen  in 
benzenoid  compounds  by  CH3,  Br,  NH2,  NO2,  &c.     Reference  may  here  be  made 
to  a  paper  by  G.  Kriiss  [Ber.  15.  1243,  and  16.  2051]  on  an  optical  method  for 
determining  whether  or  not  chemical  action  has  occurred  between  two  substances 
in  solution,  all  the  possible  products  of  the  reaction  being  also  soluble  under  the 
experimental  conditions.     The   method   consists,  essentially,  in   comparing   the 
sums  of  the  absorption-spectra  of  the  original  liquids  with  the  absorption-spectrum 
of  a  mixture  of  these  liquids. 

2  It   may  be  well  to  gather  together   here  references  to  the  most  important 
articles  and  papers  on  the  subject  of  this  section: — KOPP,  Annalen  96.  153,  303; 
100.   19,  &c.     BUFF,  Annalen   Supplbd.   4.    129,  and  Ber.  4.    647.     THORPE, 
C.  S.  Journal,  Trans,  for  1880.  141,  327.    L.  MEYER,  Annalen  Supplbd.  5.  129; 
also  Die  modernen    Theorien   (4th  Ed.),   284 — 292  ;   English   Ed.  pp.  259-267. 
ELSASSER,  Annalen  218  302.     STAEDEL,  Ber.  15.  2559.     WEGER,  Annalen  221. 
61.     RAMSAY,    C.   S.  Journal,  Trans,  for  1879.  463 ;  do.    for  1881.  49.    66. 
LOSSEN,  Annalen  214.  81.    Compare  also  SCHIFF,  Ber.  14.  2761;  15.  1270;  19. 
560;  Annalen  220.  71,   278;  223.  247.     SCHALFEJEW,  Ber.  15.  2209;   16.   1853. 
ZANDER,  Annalen,  224.  56.    LOSSEN  and  ZANDER,  Annalen,  225.  rog.     LOSSEN, 
Annalen,  243.  64.     GARTENMEISTER,  Annalen,  233.  249.     HORSTMANN,  Ber.  19.* 
1591;  20.  766.     ISCHERMAK,  Annalen,  112.   129;    114.  25.     SCHRODER,   Wied. 
Ann.  11.  997;  14.  656;  KRAFFT,  Ber.  15.    1687.     VOLLMAR,  Ber.  15.   2560. 
WILSON,  Proc.  R.  S.  32.  457.     NEUBECK,  Zeitschr.fiir  physikal.  Chemie,  1.  649. 
See  also  O.  E.  Meyer's  Die  Kinetische  Theorie  der  Case,  216— 221  :  and  WATTS' 
Diet.;  1.  440  el  seq.  and  (more  especially)  3rd  Supplt.  2117  et  seq. 


3l8  PHYSICAL   METHODS.  [BOOK  I. 

expressed    in    terms  of  the   same    standard.      The  value  of 

formula-weight  .  . 

— r^—  is  equal  to  the  product  of  specific   volume 
spec,  gravity 

multiplied  into  molecular  weight,  assuming  the  latter  to  be 
the  same  as  the  formula-weight;  or  we  may  say  that,  if  the 
weight  expressed  by  the  formula  is  taken  in  grams,  the  quo- 
formula-weight  ,,  r      ,. 
tient  -              — jS —   represents  the  number  of  cubic  centi- 
spec.  gravity 

metres  occupied  by  an  amount  of  the  substance  in  grams 
proportional  to  its  molecular  weight.  Now  we  can  deter- 
mine the  molecular  weights  of  gaseous  compounds  only : 
if  the  specific  gravities  of  compounds  are  referred  to  hydro- 
molecular  weight 

gen    as    unity,    then,    -  — r~ —  =  const.  =  2.     Never- 

spec.  gravity 

•r     1  ^-     i.    formula-weight    .        .  .   .      ... 

theless,    if  the   quotient   ^ —    is    obtained   for   a 

spec,  gravity 

number  of  liquid  compounds,  we  shall  have  a  series  of  com- 
parable values,  which — if  formula-weight  of  liquid  is  a  simple 
multiple  of  molecular  weight  of  gas — represent  the  volumes 
occupied  by  quantities  of  various  liquid  compounds  pro- 
portional to  the  molecular  weights  of  the  same  compounds 
in  the  state  of  gases. 

The  meaning  to  be  attached  to  the  expression  'volume 
occupied  by  a  quantity  proportional  to  molecular  weight ' 
will  be  discussed  in  paragraph  156. 

The  name  atomic  volume  is  generally  applied  to  the  quo- 
atomic  weight 

tient  —          — r- ? — ~n — = —    —  (water  =  i). 

spec,  gravity  of  solid  element 

The  determinations  of  the  specific  gravities  of  liquids 
necessary  for  finding  values  for  the  quotient  we  are  discussing, 
should  be  made  under  comparable  conditions ;  this  is  roughly 
fulfilled  by  determining  the  specific  gravities  at  the  boiling 
points  of  the  liquids1. 


1  It  would  be  advisable  to  compare  those  volumes  of  liquids  for  which 
temperature  and  pressure  are  equal  fractions  of  their  critical  values.  (See 
Ostwald's  Lehrbttch,  1.  336.)  Full  details  regarding  the  methods  used  for  de- 
termining the  spec.  grav.  of  liquids  at  their  boiling  points  will  be  found  in  Thorpe's 
paper,  loc,  cit.;  see  also  Ramsay  (loc.  cit.) ;  Schiff  (loc.  cit.);  and  Neubeck  (loc.  cit.). 


CH.  IV.  §§  150,  151]      MOLECULAR   VOLUMES.  319 

Let  the  molecular  volume,  i.e.  the  quotient 

formula-weight  of  liquid  compound 
spec,  gravity  referred  to  water 

be  expressed  by  the  symbol  (  V}.  Then  the  value  of  (  F)  for 
a  compound  is  in  some  cases  equal  to  the  sum  of  the  values 
of  (  V)  for  the  elementary  atoms  which  form  the  molecule  of 
that  compound.  But  is  (F)  always  the  sum  of  the  atomic 
volumes  of  the  constituent  elements,  and  has  each  elementary 
atom  a  constant  value  ? 

For  many  carbon  compounds  Kopp  has  shewn  that 


But  in  some  cases  the  observed  value  of  (  V)  does  not  agree 
with  that  calculated  by  this  formula;  thus 


Aldehyde    C2H4O  :    calculated    (V)  =  (2  .  ii)  +  (4- 

observed  (V)  =S^'5-    +47 


Acetic  acid  C2H4O2  :  calculated  (F)  =  (2  •!!)  +  (4-  5'5)  +  (2-7'8)  =  59'6 

observed  (F)  =63-5.    +3-9 

The  value  of  (  V]  for  a  compound  CxHvOt  is  conditioned, 
according  to  Kopp,  by  the  value  of  (  F)  for  the  oxygen  atom, 
or  atoms,  in  the  molecule.  Kopp  gives  the  following  two 
values,  according  as  the  oxygen  atom  acts  as  a  monovalent  or 
divalent  atom  in  the  given  molecule1;  — 


Applying  these  values  to  the  case  of  aldehyde,  we  have 

(2.ii)  +  (4.  5-5)+  12-2-56-2; 


a  result  which  agrees  very  closely  with  the  observed  value, 
viz.  56-5.     For  acetic  acid  we  have 


I2'2  =  64'o:   observed  =  63-5. 
^OH 

1  Kopp  used  the  expression  'oxygen  within  the  radicle'  as  synonymous  with 
what  is  now  called  divalent  (singly-linked)  oxygen  atoms;  and  'oxygen  without 
the  radicle'  as  synonymous  with  monovalent  (doubly-linked)  oxygen  atoms. 


32O  PHYSICAL   METHODS.  [BOOK  I. 

Or  again,  for  ethylic  acetate, 
O 


O  —  C2H5 

observed  ==  107*8. 

Or,  once  more,  for  acetone  and  its  isomeride  allylic  alcohol, 

(i)  (F)H3C  —  C  -CH,  =  (3.n)  +  (6.  5-5)+  12-2  =  78-2:  observed  =  78-0; 
I 
O 


(2) 

H      H2 

Instead  of  assigning  two  values  to  the  oxygen  atoms  in 
compounds  of  the  form  Q-H^O.,,  it  would  probably  be  better  to 
employ  the  value  (  V]  €0  =  23-2  (i.e.  11  +  12-2),  which  attri- 
butes the  influence  on  the  total  value  of  (  F)  due  to  the 
presence  of  the  group  CO  to  both  the  atoms  which  com- 
prise this  group. 

Schiff  (loc.  cit.}  concludes  that  the  value  of  (F)  O"  varies 
according  to  the  nature  and  arrangement  of  all  the  con- 
stituents of  the  molecule  ;  and  also,  that  the  value  of 
(  F)  X  -  C  -  O  is  always  greater  than  that  of  (  F)  C  -  O  -  X, 
where  X  represents  a  radicle. 

Kopp1  deduced  two  values  for  (F)S;  thus  (F)SI  =  28'6, 
(F)Sn  =  22'6:  but  only  one  value  for  (  F)C,  and  one  for 
(F)H  and  (F)C1.  Many  and  very  varying  values  have 
been  found  by  different  observers  for  (  F)N  :  thus  Kopp 
assigns  the  value  2-3  to  (  F)N  when  N  occurs  in  amines,  and  17 
when  N  occurs  in  CN  and  in  some  nitro-compounds;  Ramsay 
gives  (F)N  =  3'6  in  amines,  =  9-0  in  pyridine,  lutidine,  &c., 
and  =  7  in  aniline,  toluidine,  and  dimethylaniline. 
152  If  the  influence  exerted  by  the  oxygen  in  a  carbon  com- 
pound on  the  value  of  (  V)  for  that  compound  varies  accord- 
ing to  the  actual  valencies  of  the  oxygen  atoms  in  the  mole- 
cule, it  appears  probable  that  the  total  value  of  (  V]  will  also 
depend  on  the  actual  valencies  of  the  carbon  atoms  in  the 
molecule.  Buff2  thought  that  his  determinations  shewed  that 
the  value  of  (  F)  for  compounds  containing  trivalent  (doubly- 

1  See  also  Ramsay,  C.  S.  Journal  Trans,  for  1879.  471  —  i. 

2  Annalen,  Supplbd.  4.  143  et  seq. 


CH.1V.  §§  152,  153]        MOLECULAR   VOLUMES.  321 

linked)  carbon  atoms  is  greater  than  the  value  calculated  on 
the  assumption  that  ( V}Cni  =  ( F)CIV  =  1 1.     Thus, 

(1)  DichlorethyleneCUzzC1"  — CUI-H2,  (^  =  79-9: 

(F)  calculated  =  78-6;  diff.=  +  i'3. 

(2)  Carbon  dichloride  CL  —  C"1  —  C"1  —  C12,  ( V)  =  1 1 5-4  : 

(V)  calculated=H3'2;  diff.=  +  2'2. 
H3CIV 

(3)  Amylene  ^  >Cni  —  C'"  -  CIVH  3,  ( F)  =  1 1 2  : 

H3CIV  H 

"  ( V)  calculated  =  1 10  ;  diff.=  +2*0. 

(4)  Valerylene  H3C    —  CIU  —  C"  —  Cm  —  CIVH, ,  ( V)  =  104-0  : 

H  H 

(V)  calculated  =  99;  diff. 


322  PHYSICAL  METHODS.  [BOOK  I. 

also  vary,  apparently,  in  accordance  with  the  distribution  of 
the  interatomic  reactions  in  molecules  wherein  all  the  carbon 
atoms  are  tetravalent,  and  all  the  oxygen  atoms  are  divalent. 
Thorpe  (loc.  cit.}  has  given  some  examples  of  such  variations; 
but  Zander1  has  extended  the  number  of  examples  con- 
siderably. Thus  a  comparison  of  (  V)  for  propyl  and  isopropyl 
compounds  shews  that  the  normal  compounds  always  exhibit 
a  smaller  value  than  the  iso-compounds  :  — 

C3H7OH    C3H7I    C3H7Br     C3H7C1 

highest  value  of  (  V)  obtained  for  normal  \ 

/H.C  —  C  —  C—  X\       \        81-4     108-2     97-5       917 
compound^    3       H2    H2         )       ) 

lowest  value    of  (  F)   obtained  for  iso- 


compound     X-CH       3]  f        82>3      ^S     99'o 


But  the  molecules  of  both  classes  of  compounds  contain  only 
tetravalent  carbon  atoms2. 

Lossen3  has  collected  the  most  trustworthy  data  bearing 
on  the  question  as  to  whether  or  not  a  constant  value  can  be 
assigned  to  (F)CH2.  Kopp  gave  22  as  the  mean  value  for 
this  group.  Lossen  shews  that  the  differences  between  the 
values  of  (F)  for  successive  homologues  of  the  acid  series 
CnH2n+1CO2H  nearly  agree  with  the  differences  calculated  on 
the  basis  of  (F)CH2=22;  but  that  in  the  series  of  alcohols 
CnHwlCH2OH  the  value  of  (F)CH2  varies  from  187  to  21, 
assuming  that  the  other  atoms  exert  a  constant  influence  on 
the  total  value  of  (  V).  Apparently  then  a  variable  value 
must  be  assigned  to  (F)CIV,  or  to  (  F)H,  or  to  both  of  these 
quantities. 

Some  light  is  thrown  on  this  point  by  Zander's  comparison 
(loc.  cit^)  of  (  F)  for  propyl,  isopropyl,  and  allyl,  compounds, 
which  leads  to  the  conclusion  that  the  difference  between  (  F) 
for  a  normal  propyl  and  the  corresponding  allyl  compound, 
i.e.  between  two  compounds  differing  in  composition  by  H8, 
varies  from  57  to  8'9  (having  a  mean  value  of  7'i):  hence,  if 

1  Annalen  'OA.  138:  224.  56. 

2  See  also  Brown  Proc.  R.  S.  26.  238.     Also  Elsasser,  Annalen  218.  302. 
8  Annalen  214.  8r  et  seq. 


CH.  IV.  §153]  MOLECULAR  VOLUMES.  323 

we  assume  that  the  difference  in  question  is  wholly  due  to  the 
difference  in  empirical  composition,  we  appear  forced  to  con- 
clude that  the  value  of  the  influence  exerted  on  (  V)  by  the 
monovalent  atom  H  is  variable1. 

Thorpe  (loc.  cit.}  got  these  results  for  compounds  containing 
only  tetravalent  carbon  atoms  in  their  molecules:  — 
H2CC12(F)=  65-12;  hence  (F)Cl  =  2i-6;  (assuming  (F)C=u, 


HCC13(F)=  84-53;      „ 
CC14(^)  =  103-68;      „ 
Taking  the  mean  value  for(F)Cl,  viz.  22-5,  and  applying  this 
to  calculate  the  values  of  (  V]  for  each  of  the  preceding  com- 
pounds, we  have 

(F)H2CClo=  67-0        observed=  65-12        diff.=  -r88 

(F)HCCl^  84-0  „        =  84-53          „    =+   -53 

(V)     CCl4=ioro  „        =103-68          „    =+2-68 

Hence  the  value  of  (  F)C1  appears  to  be  variable.    This  is  more 

strikingly  illustrated  by  Staedel's  comparison2  of  the  differences 

in  the  values  of  (  F),  and  also  the  differences  in  the  boiling 

points,  at  various  pressures,  of  chlorine  compounds  derived 

from  C2H4. 

The    differences   in  (F),  and    also   in  B.P.,  between  the 
following  pairs  of  compounds,  viz. 

C1H2C  —  CH2C1  and  H3C-CH2C1, 
C1H2C  —  CHC12  and  H3C  —  CHC12, 
C1H2C  —  CC18  and  H3C  —  CC13, 

1  Besides  the  empirical  difference  of  H2,  there  is  a  difference  in  the  actual 
valencies   of   some   of   the    carbon    atoms   in    propyl    and    allyl    compounds  ; 
thus,    normal    propylic  alcohol   is   H3C  —  C  —  C  —  OH,   and   allylic  alcohol   is 

H2   H2 
H2Cni—  C1"—  C—  OH.     See  also  Weger,  Annalen  221.  61,  who  gets   different 

H       H2 

values  for  (  V)  CH2  in  different  series  of  compounds.  See  Ber.  16.  2458,  where 
Kopp  reminds  us  that  this  number  was  given  by  him  as  a  mean  value,  and 
nothing  more.  Schiff  (Annalen  220.  286,  and  291)  concludes  that  (F)C  almost 
certainly  varies  according  to  the  nature  and  the  arrangement  of  the  constituents  of 
the  molecule  in  which  C  occurs.  Horstmann  (Ber.  20.  766)  collects  many  data 
which  lead  him  to  the  conclusion  that  '  unsaturated  compounds  with  closed  chain 
formulae  have  considerably  smaller  molecular  volumes  than  those  with  open  chain 
formulae  and  multiple  linkings  of  atoms  '.  Neubeck  (Zeitschr.  fur  physikal.  Chemit, 
1.  649)  shews  that  (V]  for  benzene  derivatives  is  modified  according  to  the 
position  [ortho,  meta,  or  para]  of  the  replacing  groups. 

2  Ber.  15.  2559. 

21  —  2 


324  PHYSICAL  METHODS.  [BOOK  I. 

express  differences  corresponding  with  change  of  CH3  into 
CH2C1,  i.e.  with  the  introduction  of  the  first  chlorine  atom  in 
place  of  an  atom  of  hydrogen  into  the  hydrocarbon  residue 
CH, 

The  differences  in  the  values  of  the  same  quantities  be- 
tween the  following  pairs  of  compounds,  viz. 

CLjHC  —  CH,  and  H2C1C  —  CH3, 
C12HC  —  CH2C1  and  H2C1C-CH2C1, 
C12HC  —  CHC12  and  H2C1C  —  CHC12, 
C12HC  —  CC13  and  H2C1C  —  CC13, 

express  differences  corresponding  with  the  introduction  of  the 
second  chlorine  atom  (in  place  of  an  atom  of  hydrogen)  into 
the  residue  CH8. 

And  lastly,  by  comparing  (  V)  and  B.P.  for  the  following 
pairs  of  compounds,  viz.: 

C13C  —  CH3  and  C12HC-CH3, 
C13C  —  CH2C1  and  C12HC-CH2C1, 
C13C  —  CHC12  and  C12HC  —  CHC12, 
C13C  —  CC13  and  C12HC  —  CC13, 

the  differences  corresponding  with  the  introduction    of  the 
third  chlorine  atom  into  the  group  CH8  are  determined. 
Now  the  differences  in  question  are: 


for  the  first  chlorine  atom  (V}=  14-20:  B.P. 

second       „  (F)=  16-37:  B.P.  =  3i°'3o; 

„       third          „  (  V}=--  19-16:  B.P.  =  i6°-o4. 

Hence  each  chlorine  atom  has  a  different  'volume-value' 
and  a  different  'boiling-point-value'.  If  we  choose  to  at- 
tribute the  observed  differences  to  the  carbonaceous  parts  of 
the  molecules,  i.e.  to  C2H4  in  C2H4G12,  to  C2H3  in  C2H3C13>  &c., 
we  seem  still  obliged  to  admit  that  carbon  and  hydrogen 
atoms  have  varying  'volume-values',  and  varying  'boiling- 
point-values  ',  in  the  molecules  formulated. 

154  The  remark  made  in  paragraph  1  5  1  that  the  value  of  (  F) 
for  a  compound  is  equal  to  the  sum  of  the  values  of  (  V]  for 
each  of  the  elementary  atoms  in  the  molecule  of  that  com- 
pound, must  evidently  be  supplemented  by  the  statement, 
that  in  the  case  of  carbon  compounds,  at  any  rate,  the  value 
of  (  V}  is  not  constant  for  C  or  O,  and  probably  not  for  H  or 


CH.IV.  §§  154,  155]      MOLECULAR   VOLUMES.  325 

Cl,  but  varies  in  accordance  with  (i)  the  actual  valencies  of 
the  atoms  of  carbon  and  oxygen,  and  (2)  the  distribution  of  all 
the  atomic  interactions  in  the  molecule.  The  precise  character 
of  the  connexion  between  the  values  of  ( V)  for  C,  O,  H,  and 
Cl,  and  the  valencies  on  the  one  hand,  and  the  nature 
of  the  atoms  (or  atomic  groups)  in  direct  union  within  any 
molecule  on  the  other  hand,  cannot  be  ascertained  until 
much  more  experimental  data  has  been  accumulated1.  The 
known  data  regarding  the  values  of  ( V)  cannot  therefore  be 
applied  in  other  than  a  very  tentative  way  to  the  selection  of 
one  from  among  several  possible  structural  formulae2. 
55  The  values  of  ( V)  for  many  solid  compounds  have  been 
compared,  and  attempts  have  been  made  to  generalise  the 
relations  between  these  values;  but,  as  might  be  expected 
from  considering  how  little  comparable  are  the  conditions 
under  which  the  relative  densities  of  solids  have  been  deter- 
mined, the  conclusions  are  either  vague  and  difficult  of  precise 
application,  or  represent  only  interesting  relations  between 
certain  numbers,  without  much,  if  any,  connexion  with 
chemical  facts. 

By  considering  the  difference  between  (F)MO  and  ( F)M, 
a  fairly  constant  value  for  (  F)O  in  the  oxides  is  sometimes 
obtained:  thus  for  PbO  and  Fe2O8,  the  difference  in  question 
is  about  5-5.  But  in  other  oxides  the  value  of  (  F)O  appears 
to  be  very  variable ;  thus, 

(F)CuO-(F)Cu  =  5'i;  but  (F)  CuoO-(F)  Cu2=  10-5. 
Brauner  and  Watts3  have  drawn  the  following  conclusions 

1  It  is  pointed  out  by  Lossen  (loc.  cit.)  that  careful  determination  of  ( V)  for 
many  series  of  carbon  compounds  and  for  many  individuals  in  each  series,  are 
now  required. 

2  An  illustration  of  the  difficulties  which  are  'met  with,  and  of  the  uncertain 
nature  of  the  results  obtained,  is  furnished  by  the  contradictory  conclusions  of 
Thorpe  (see  Watts's  Diet,  3rd  Supplt.  2117 — 18)  and  of  Masson  and  Ramsay  (see 
C.  S.  Journal  Trans,  for  1881,  51  et  sey.)  regarding  the  structural  formula  of  POC1:). 
Thorpe  concludes  that  the  formula  ought  to  be  written  C12=P— O  — Cl,  Masson 
•and  Ramsay  think  that  C13~  P — O  more  nearly  represents  the  facts.    In  connexion 
with  the  formula  of  this  compound  see  the  experiments  of  Michaelis  and  La  Coste 
(Ber.  18.  2118). 

3  Phil.  Mag.  [5]  11.  60. 


326  PHYSICAL   METHODS.  [BOOK  I. 

from  comparisons  of  (F)MO  and  (F)M  for  different  series 
of  oxides. 

(1)  In  strongly  basic  oxides  the  value  of  (  F)O  is  nega- 
tive ;  the  more  basic  the  oxide,  and  the  greater  the  value  of 
(  F)M  in  the  oxide,  the  more  negative  is  the  value  of  (  F)O. 

(2)  In  oxides  of  heavy  metals  and  non-metals  the  value 
of  (  F)O  is  positive. 

(3)  In  oxides  of  the  earth  metals  the  value  of  (V)O 
is  nil. 

The  values  of  (  F)  for  isomorphous  compounds  generally 
vary  little;  thus, 

(F)MgO.Al2O3  =  4i'4  (V)  ZnO  .Fe2O3  =  47'o 

(  V}  ZnO  .  Al2O3  =  4o-2  (F)  MnO  .  Cr2O3=46'4. 

The  greater  the  agreement  between  the  angles  of  crystals 
belonging  to  the  same  class,  the  less  do  the  values  of  (  V} 
differ,  e.g. 

((V\  ptc°3=4r2  }  Crystals  are  alm°St  identical 

(V)  BaCO3=45'S    crystals  exhibit  differences1  from  those  of  SrCO3  and 
PbC03. 

Kopp2  has  concluded  that  if  D,  the  difference  between 
what  he  calls  the  '  molecular  volumes  '  of  two  isomorphous 

(V}  —  (V} 

compounds,  is  represented  as   D  =  YJTJ/\  —    J7\~\  »  then   the 

" 


value  of  D  may  attain  a  maximum,  equal  to  0*328,  without 
isomorphism  being  impossible. 

Determinations  of  (  V}  for  anhydrous  and  hydrated  salts 
promise  to  throw  some  light  on  various  questions  implied  in 
the  commonly  used  expressions  'water  of  crystallisation'  and 
'  water  of  constitution  '. 

Graham  distinguished  '  saline  '  water  from  '  basic  '  water  in 
salts  and  acids  ;  the  replacement  of  the  former  by  another  salt, 
or  by  an  oxide,  produced  a  double  salt,  or  in  the  case  of  acids 

1  For  more  details  see  Naumann's  Handbuch  der  Allgeineinen  und  Physikal- 
ischen  Chetnie,  360  —  362. 

2  Annalen  36.  r.    Fogg.  Ann.  52.  262;   53.  446;   56.  371.     See  also  article 
"  Isomorphie  ",  in  the  News  Handworterbiuh  der  Chetnie. 


CH.IV.  §155]  MOLECULAR  VOLUMES.  327 

a  normal  salt;  the  replacement  of  the  'basic'  water  in  an  acid 
produced  a  basic  salt.     Thus, 

MgSO4  H2O  6H2O   gave    MgSO4  K2SO4  6H2O; 

saline     basic 

N2O5  H2O  3H2O  gave  f  N2O5  CuO  3H2O  normal  nitrate  of  copper. 

CuO    3CuO    basjc 


3H2O  gave  f  N2 

basic  j  j 


Graham  further  distinguished  basic  water  from  water  of 
constitu  tion  ;  e.g  . 

H2SO4.H2O,    from   C2O3.H2O. 

basic  constitutional 

Thorpe  and  Watts1  have  determined  (F)  for  the  salts 
MSO4,  when  M  =  Mg,  Zn,  Cu,  Mn,  Fe,  Co  ;  and  for  the  hy- 
drated  salts  MSO^H2O  when  M  =  Mg,  Zn,  &c.  and  x  varies 
from  i  to  7. 

The  value  of  (  F)MSO4  was  found  to  be  independent  of 
the  nature  of  M  for  the  dehydrated  salts.  The  difference 
(  F)MSO4.;trH2O-(  F)MSO4gave  the  increase  in  (  V]  for;trH2O 
added  to  the  salts.  The  following  results  were  obtained. 

Mean  difference  between  values  of 


and  (F)S.H2O  =107 
(F)S.H20  „  (F)S.2H20=i3'3 
(F)S.2H20  „  (J/)S.3H20=i4-5 
(F)S.3H20 
(F)S.6H2O 


Hence  the  value  of  (F)MSO4.^H2O  is  changed  to  a 
different  amount  by  each  of  the  molecules  of  water  which 
combines  with  the  salt;  or,  it  may  be  said,  that  the  water 
molecules  contribute  in  unequal  degrees  towards  the  total 
value  of  (  F). 

Clarke2  has  compared  the  differences  between  (F)  for 
hydrated  and  (  V}  for  dehydrated  salts,  belonging  to  two 
classes  of  compounds. 

In  the  first  class,  when  M  =  Ca,  Sr,  Ba,  Mg,  Cu,  Fe,  or  Co, 
and  x  varies  from  2  to  6,  the  mean  value  of 


1  C,  S.  Journal  Trans,  for  1880.  102. 

*  Amer,  Journal  of  Sci.  and  Arts,  (3).  8.  428. 


328  PHYSICAL   METHODS.  [BOOK  I. 

was  found  to  be=  1376  (with  a  maximum  value  of  15-0,  and 
a  minimum  of  12-5). 

The  second  class  comprised  various  hydrated  oxides  and 
hydroxides,  viz. 

B2O33H2O,   I2O6H2O,   K2OH2O,   CuOH2O,   SrOH2O,   BaOH2O, 
A1203H2O,    Mn203H2O,   Fe2O3H2O. 

In  this  class  the  value  of  the  difference 

( V)  oxide  *H2O  -  ( V)  oxide 

x 
varied  from  7*4  to  IQ'4. 

If  S  represent  one  of  the  chlorides  belonging  to  the  first 
class,  or  one  of  the  oxides  belonging  to  the  second  class,  then, 
for  class  I,  the  formula  (F)S  ^H2O  =  (  F)S  +  (x .  1376)  gives 
numbers  which  agree  fairly  well  with  the  observed  results;  but 
no  such  simple  relation  between  (  F)S  ^H2O  and  (  F)S  can  be 
traced  among  the  results  obtained  for  compounds  belonging 
to  class  II. 

But  the  hydrates  of  class  I  belong  to  the  group  of  com- 
pounds containing  'water  of  crystallisation',  whereas  those 
of  class  II,  or  most  of  them  at  any  rate,  belong  to  the  group 
containing  'water  of  constitution';  hence,  although  the  results 
obtained  by  Thorpe  and  Watts  (loc.  cit.}  lead  to  the  conclusion 
that  the  value  of  (F)H2O  in  the  salts  MC1^H2O  is  probably 
different  for  each  addition  of  H2O,  nevertheless  Clarke's  num- 
bers, taken  as  a  whole,  emphasise  the  difference  between 
'water  of  crystallisation'  and  'water  of  constitution',  and  shew 
that  the  chemical  difference  implied  in  these  expressions  is 
connected  with  the  relative  magnitudes  of  the  spaces  occupied 
by  chemically  comparable  quantities  of  the  hydrated  salts 
belonging  to  each  class  of  compounds. 

formula-weight  ,       , 

156        The  quotient  r^ —        .,     has  been  treated  as  an  empi- 

specmc  gravity 

rically  determined  quantity;  incidentally  it  has  been  regarded 
as  expressing  the  volume  occupied  by  a  quantity  of  the  com- 
pound formulated  proportional  to  the  mass  of  the  molecules 
which  form  the  vapour  of  that  compound.  The  question  is 
often  propounded  in  papers  on  'Specific  volumes',  whether  the 


CH.  IV.  §156]  MOLECULAR  VOLUMES.  329 

volume  of  an  element  in  the  free  state  is,  or  is  not,  identical 
with  the  volume  of  the  same  element  in  combination.  This 
question,  it  seems  to  me,  may  be  better  put  in  another  form. 
What  is  the  connexion  between  the  value  of  (  V)  for  a  given 
compound,  and  the  nature  and  arrangement  of  the  atoms 
which  constitute  the  molecule  of  that  compound  ?  It  has  been 
shewn  (pars.  152,  153)  that  the  partial  value  to  be  assigned  to 
each  atom  is  not  a  constant  quantity;  in  other  words  tha.t(V) 
varies  with  variations  in  the  arrangement,  no  less  than  in  the 
nature,  of  the  atoms  which  form  the  molecule  of  the  com- 
pound for  which  (  V)  has  been  determined.  But  is  there  any 
connexion  between  the  variations  of  (  V),  the  valencies  of  the 
atoms  on  the  one  hand,  and  the  distribution  of  the  interatomic 
reactions  on  the  other  ?  From  the  data  concerning  isomeric 
carbon  compounds,  firstly,  containing  only  saturated  poly- 
valent atoms,  and  secondly,  containing  also  unsaturated  poly- 
valent atoms,  we  may  conclude,  I  think,  that  both  connexions 
exist.  It  seems  probable  that  a  decrease  in  the  actual  valency 
of  an  atom,  other  things  remaining  the  same,  is  attended  by 
an  increase  in  the  value  of  (  V).  But  Staedel's  investigation 
(par.  153)  shewrs  that  the  latter  value  is  also  modified  by  the 
nature  of  all  the  atoms  in  the  molecule.  If  these  connexions 
can  be  made  precise,  and  their  nature  ascertained  by  careful 
investigation,  it  may  become  possible  to  trace  relations  be- 
tween the  volumes  occupied  by  molecules  of  defined  structure 
and  the  energy-differences  of  these  molecules,  and  perhaps  to 
connect  with  these  the  differences  in  the  values  of  the  refrac- 
tive, and  the  rotatory,  powers^of  the  same  molecules1. 

If  the  value  of  (V)  for  a  compound  is  regarded  from  the 
point  of  view  of  the  molecular  theory,  a  connexion  may  be 
traced  between  this  value  and  the  partial  value  of  (  V]  for  each 
atom  in  the  molecule  of  the  compound.  For  it  has  been  shewn 


1  We  should  thus  gain  clearer  conceptions  of  the  properties  of  atoms  as  these 
are  exhibited  in  atomic  interactions,  and  also  be  able  to  connect  these  interactions, 
in  a  more  precise  manner  than  is  yet  possible,  with  the  properties  of  the  systems 
thereby  formed.  If  this  view  is  accepted  it  is  evident  that  the  results  obtained  by 
the  various  physical  methods  discussed  in  this  and  the  preceding  section  must 
have  kinetical  as  well  as  statical  aspects  (see  Book  H.). 


330  PHYSICAL  METHODS.  [BOOK  I. 

by  L.  Meyer1,  and  by  Loschmidt2,  that  the  spaces  occupied 
by  gaseous  molecules  (calculated  from  data  based  on  the 
transpiration-coefficients  of  the  substances)  are  connected  with 
the  atomic  structure  of  these  molecules,  in  the  same  general 
way  as  has  been  shewn  by  Kopp  and  others  to  hold  in  the 
case  of  liquid  compounds3.  The  Clausian  sphere-of-action 
(ivirkungsspliare)  of  a  molecule  is  the  smallest  space  which  the 
molecule  can  occupy  under  given  conditions.  Changes  in 
these  conditions  (e.g.  change  of  temperature),  changes  in  the 
form  of  the  molecule,  or  changes  in  the  arrangement  of  the 
atoms  in  the  molecule,  will  be  accompanied  by  changes  in  the 
space  occupied  by  the  molecule.  The  relations  between  the 
values  of  these  smallest  spaces  (spheres-of-action)  occupied  by 
the  molecules  of  two  gases  can  be  calculated,  by  means  of  a 
formula  deduced  from  the  general  principles  of  the  molecular 
theory,  from  observations  of  the  transpiration-coefficients  of 
the  gases.  Putting  the  experimentally  determined  value  of 
(  F)  as  the  value  of  the  molecular  sphere-of-action  of  one  of 
the  gases,  the  values  of  the  molecular  spheres-of-action  of  other 
gases  can  be  found,  and  compared  with  those  calculated  from 

T;r        >     T./T        i          ,  T  •  i  »         i         r      atomic  weight 

Kopp  s,  Meyer  s.  and  Loschmidt  s,  values  for ^ ^— 

specific  gravity 

of  nitrogen,  oxygen,  hydrogen4,  &c.,  and  from  the  partial  values 
assigned,  by  different  chemists,  to  various  atoms  in  determining 
the  total  value  of  ( V)  for  molecules  containing  these  atoms. 
This  is  done  by  O.  E.  Meyer  (loc.  cit.  pp.  219 — 221).  The 
observed  and  calculated  values  of  (V)  agree  as  closely  as 
could  be  expected,  considering  that  regard  has  been  paid  in  the 
calculations  solely  to  volume,  whereas  the  molecular  spheres- 
of-action  must  be  conditioned  by  the  form,  the  diameter,  and 
the  length,  of  the  molecular  systems.  Hence  there  is  a  well- 
established  probability  in  favour  of  the  conclusion  that  the 
partial  values  assigned  to  the  different  atoms,  in  determining 

1  Annalen,  Supplbd.  5.  129. 

2  Sitzberichte  der  K.  Akad.  zu  Wien  (mat/i.-naturwiss.  dasse).  52.  (2nd  part)  395. 
8  See  O.  E.  Meyer's  Die  Kinetische  Theorie  der  Case,  216 — 221. 

4  For  a  description  of  the  determination  of  this  constant  for  oxygen  and  other 
gases  from  measurements  of  the  transpiration-coefficients  of  these  gases,  see 
L.  Meyer,  Annalen,  Supplbd.  5.  129. 


CH.  IV.  §§  156,  157]  ETHERIFICATION.  33! 

the  total  value  of  (  V}  for  a  liquid  compound,  are  proportional 
to  the  volumes  occupied  by  these  atoms  in  the  gaseous  state. 
But  this  is  just  the  conclusion  drawn  from  an  empirical  study 
of  the  values  of  (  V)  determined  for  series  of  liquid  compounds. 
Much  work  must  however  be  done  before  precise  connexions 
can  be  traced  between  the  total  value  of  ( V}  and  the  partial 
values  assigned  to  the  various  atoms  in  any  molecule. 

It  has  generally  been  assumed  that  the  volumes  of  differ- 
ent liquids  are  under  comparable  conditions  at  the  boiling 
points  of  the  liquids;  but  van  der  Waal's  investigations1  have 
shewn  that  those  volumes  of  liquids  are  comparable  for  which 
temperature  and  pressure  are  equal  fractions  of  their  critical 
values.  In  order  therefore  to  compare  molecular  volumes— 
i.e.  to  compare  values  of  (  V] — it  would  be  advantageous  to 
determine  by  experiment  the  critical  temperature  and  pres- 
sure of  the  liquid  compounds  examined.  This  has  been  done 
in  very  few  cases;  but  until  it  is  done,  considerable  doubt 
must  be  thrown  on  the  value  of  the  elaborate  deductions 
which  have  been  drawn  from  the  data  regarding  molecular 
volumes8. 


SECTION  IV.     Method  based  on  the  determination  of 
'  Etherification-values!* 

157        The  rate  of  formation  of  ethereal  salts  by  the  mutual 
actions  of  alcohols   and   carbon-containing   acids   has   been 

1  Die  Continuitiit  des  gasformigen  und  fliissigm  Zustandes.     (Leipzig,  1881). 
Comp.  Ostwald's  Lehrbuch,  1.  336 — 339. 

2  Neubeck's  results  (Zeitschr.  fur  physikal.   Chemie,   1.  649)  shew  that  the 
relations  which  exist  between  the  molecular  volumes  of  various  benzene  deriva- 
tives at  ordinary  pressures  also  hold  good  at  pressures  of  450  and  200  mm. 

3  The   papers  by   Menschutkin,  of  which   this   section  is   a  very  condensed 
summary,  will  be  found  in  J.  fiir  prakt.  Chemie,  (2)  24.  49:  do.  25.  193,  and  203 
(abstracts  in  C.  S.  Journal  for  1881.  1117;  1882.  384,  485,  and  595).     Abstracts 
will  also  be  found  in  Ber.  14.  2630,  2819:  15.  162,  248,  and  721.     A  paper  con- 
taining a  summary  of  Menschutkin's  results  will  be  found  in  Ann.  Chitn.  Phys. 
(5).  30.  81.     (Abstract  in  C.  S.  Journal  for  1884.  726.)     See  also  Zeitschr.  fiir 
physikal.  Chemie,  1.  611. 


332  PHYSICAL  METHODS.  [BOOK  I. 

studied  by  Menschutkin  :  many  of  his  results  have  a  more 
direct  bearing  on  the  questions  of  chemical  kinetics,  some  of 
them  however  may  find  a  place  here.  The  standard  reac- 
tions in  terms  of  which  determinations  are  stated  are  these  : 

(i)  HCH2OH  +  CH3C02H  =  CH3CO2(CH3)  +  HOH  ; 


CH 


(2)  HC  — 


X3 


By  varying  the  alcohol  in  (i)  and  the  acid  in  (2),  comparable 
series  of  values  are  obtained  for  (i)  alcohol-acetic  system,  and 
(2)  acid-isobutylic  system.  The  number  of  molecules  of 
HCH2OH  decomposed  in  reaction  (i),  and  the  number  of 
molecules  of  HCO2H  decomposed  in  reaction  (2),  when 
equilibrium  is  established,  are  taken  as  100,  and  the  results  with 
other  alcohols  and  acetic  acid,  or  with  other  acids  and  iso- 
butylic  alcohol,  are  stated  in  terms  of  this  unit. 

The  expression  'etherification-velocity'  is  used  to  denote 
the  amount  of  action  during  one  hour;  the  expression  'etheri- 
fication-limit'  is  used  to  denote  the  amount  of  action  when 
equilibrium  is  established.  Thus  the  statement  '  the  etherifica- 
tion-velocity of  CH8CH2OH  is  67'3,  and  the  etherification- 
limit  is  95'6'  means,  that  when  equal  numbers  of  molecules 
of  CH8CH2OH  and  CH8CO2H  react,  67-3  molecules  of 
CH8CH2OH  are  decomposed  during  the  first  hour,  and  95^6 
when  the  action  ceases,  the  number  of  molecules  of  HCH2OH 
decomposed  under  similar  conditions  (at  the  close  of  the 
reaction)  being  taken  as  loo1. 

The  following,  among  many  other  numbers,  were  obtained 
by  Menschutkin. 

Alcohol-acetic  system. 

Formula  of  Alcohol.  Velocity.  Limit. 

HCH2OH  80-0  100-0 

CH3.CH2OH  67-3  95-6 

C2H5.GH2OH  66-9  96-0 

1  The  process  is  conducted  at  153°  —  154°;  the  residual  acid  is  determined  by 
titration.  Two  to  five  grams  of  alcohol  are  sufficient,  and  the  process  is  always 
applicable  except  the  ethereal  salt  produced  should  be  unstable  at  the  temperature 
of  experiment. 


CH.  IV.  §157]  ETHERIFICATION.  333 

Hence,  the  substitution  of  CH3  for  H  in  the  primary  alcohol 
H.CH^OH  appears  to  be  accompanied  by  a  decrease  in  the 
etherification-velocity  of  about  I2'5,  and  in  the  limit  of  about 

4'5- 

The  following  conclusions  are  drawn  by  Menschutkin  from 
his  determinations  of  the  reaction-values  of  the  system 
R.CH2OH  +  CH3CO2H. 

(1)  The  reaction-values  (i.e.  velocity  and  limit)  of  the 
normal   group    CnH2n41    in  the  alcohols  CnHg,mCH9OH  are 
practically  the  same. 

(2)  Isomerism  in  the  CBH2n+1  radicles  of  primary  alcohols 
influences  only  the  velocity-value,  not  the  limiting  value. 

(3)  Unsaturated  alcohols  (R  .  CH2OH)  exhibit  lower  re- 
action-values   than    saturated    alcohols ;    e.g.    the  values  for 
C2H8-CH8OH  are  smaller  than  those  for  C2HS-CH2OH. 

From  his  study  of  the  etherification  of  secondary  alcohols 
R2CHOH,  the  same  chemist  concludes  that  these  alcohols 
exhibit  lower  values  than  primary  alcohols ;  and  that  the 
same  radicle  has  smaller  values  in  a  secondary  than  in  a 
primary  alcohol.  The  limiting  value  for  tertiary  alcohols 
cannot  be  determined  on  account  of  the  occurrence  of 
secondary  changes;  the  velocities  shew  great  irregularities. 

Further  results  obtained  by  Menschutkin  shew  that  definite 
connexions,  the  precise  nature  of  which  cannot  yet  be  traced, 
exist  between  the  actual  valencies  of  the  atoms,  and  also  the 
distributions  of  the  interatomic  reactions,  in  the  molecules  of 
alcohols,  and  the  etherification-values  of  these  alcohols1. 

By  multiplying  the  limiting  value  of  each  compound  by 
the  molecular  weight  of  that  compound  (and  dividing  by  100), 
numbers  are  obtained  which  exhibit  the  influence,  on  the 
etherification-limit,  of  the  molecular  weights  of  the  members  of 
the  system  studied.  Menschutkin  gives  the  following  numbers 
as  representing  molecular  limits.  In  a  later  paper  he  calls 
these  numbers  simply  weight-limits,  in  distinction  to  the  per- 
centage limits  already  explained. 


1  For  a  more  precise  statement  of  Menschutkin's  conclusions  on  this  point  see 
abstract  in  Ber.  14.  ?8i8. 


334  PHYSICAL  METHODS.  [BOOK  I. 


Acid-isobi4tylic  system. 

Molecular      Difference  for 


Acid. 

limit. 

each  CH2. 

CH3CO2H 

40-42  v 

C2H5C02H 

5o'83\ 

10*41 

(C3H7«)C02H 

6i-i7x 

I0<34     I9.8l 

(C6HU«)C02H 

80-98  / 

9'9°=  ~^  — 

(C7H15«)C02H 

102-05^ 

21-07 

Tr^'C'3  —  — 

Mean  difference  for  each  increment  of  CH2=  10-29. 

The  value  of  the  molecular,  or  weight,  limit  for  any  mem- 
ber of  this  series  of  acids  (the  alcohol  being  isobutylic)  may 
be  found  by  the  formula, 

molecular  limit  =  40-42  +  (n-  2)  10-29; 

when  n  =  number  of  carbon  atoms  in  the  molecule  of  the 
acid. 

Thus,  in  the  acid  (C3H7")  CO2H  72  =  4,  hence 

molecular  limit  =  40-42  + (2  .  io'29)  =  6ro;  observed  value  =  6i'i7. 

Menschutkin  gives  the  expression  a  +  (n  —  2}d  for  finding 
the  molecular  etherification-limit  for  an  acid  in  any  system  of 
alcohol  arid  acids,  when  a  =  molecular  limit  for  the  first  acid 
of  the  series,  and  d-  mean  increase,  for  each  increment  of 
CH2,  in  the  molecular  limit  of  the  acids  of  the  series. 

The  rule  is,  to  the  value  of  the  limit  for  the  given  alcohol 
with  the  first  acid  of  the  series,  add  (n  —  2)  d,  that  is,  add  (;/  -  2) 
times  the  mean  homologous  difference  (i.e.  the  mean  differ- 
ence for  each  increment  of  CH2)  between  the  weight-limits  of 
the  given  acid  and  the  first  acid  of  the  series,  when  n  =  num- 
ber of  carbon  atoms  in  the  molecule  of  the  given  acid. 

Thus,  required  the  weight-limit  for  the  caproic-butylic 
system.  For  the  acetic-butylic  system  a  =  40*52,  and  d=  io-29 ; 
caproic  acid  is  C8Hn.CO2H;  therefore  the  weight-limit  re- 
quired is  40-52  +  (4.  10-29)  =  8r68. 

It  is  evident  that  the  percentage  limit  can  easily  be  found 
when  the  values  of  a  and  d  are  given.  In  the  case  in  question 
we  have, 

percentage  limit  =  —      'IOO=  70-41.     [C6HU.  CO,H  =  n6]. 


CH.  IV.  §§  157,  158]      CAPILLARY-CONSTANTS.  335 

Menschutkin  gives  the  following  values  for  a  and  d  in 
various  systems  of  alcohols  and  acids  of  the  acetic  series : 


acid-ethylic  system 

acid-propylic  „ 

acid-butylic  „ 

acid-amylic  „ 

acid-hexylic  „ 

acid-heptylic  „ 

acid-caproic  „ 


a  =  39-94 
a  =  40-23 
a= 40*42 
0  =  40-55 
«= 40-64 
0=4071 
a =40-77 


=  10-29. 


It  is  also  possible  to  vary  the  alcohol,  the  acid  remaining 
constant,  and  from  the  data  obtained  to  calculate  the  weight- 
limit  for  any  given  system1. 

From  a  comparison  of  the  etherification-values  for  primary 
secondary  and  tertiary  acids,  and  also  of  the  same  values  for 
hydroxy-  and  chloro-acids  &c.,  Menschutkin  draws  certain 
conclusions  regarding  the  connexions  between  the  variations 
in  these  values  and  the  molecular  structures  of  the  various 
acids.  For  instance,  the  velocity  of  etherification  of  the 
primary  acids  is  much  greater  than  that  of  the  secondary 
acids,  but  the  limiting  values  are  nearly  identical  in  both 
series. 

A  study  of  these  conclusions  shews  that  much  is  to  be 
hoped  for  from  the  application  of  Menschutkin's  method,  but 
that  more  data  must  be  obtained  before  we  have  precise 
knowledge  concerning  the  connexions  between  the  rate  of 
formation  of  ethereal  salts  and  the  chemical  constitutions  of 
the  interacting  alcohols  and  acids2. 


SECTION  V.     Miscellaneous  methods. 

158  That  the  ' capillarity '-constants'  of  liquid  carbon  compounds 
are  connected  with  the  chemical  constitutions  of  these 
compounds  is  apparent  from  researches  by  Mendelejeff3, 

1  See  details  in  C.  S.  Journal,  Abstracts  for  1882.  387. 

2  See  some  of  Menschutkin's  generalisations  in  C.  S.  Journal,  Abstracts  for 
1882.  485,  598:  and  an  application  to  the  formula  of  maleic  and  fumaric  acids 
in  do.  do.  1882.  383. 

8  Compt.  rend.  80.  52;  51.  97. 


336  PHYSICAL  METHODS.  [BOOK  I. 

Wilhelmy1,  and  especially  Schiff2.  The  capillarity-constants 
are  calculated  from  experimental  data  by  methods  which  need 
not  be  discussed  here  (see  abstracts  of  Scruffs  papers  in  C.  S. 
Journal,  or  see  Ostwald's  Lehrbuch,  I.  479).  SchifFs  results 
lead  to  capillarity-equivalents  for  certain  atoms,  e.g.  C  =  2H, 
O  =  3H,  Cl  =  7H,  &c.,  that  is,  they  tend  to  shew  that  n  atoms 
of  one  element  have  the  same  partial  value  in  the  capillarity- 
constant  of  a  series  of  compounds  as  m  atoms  of  another 
element.  The  capillarity-equivalent  of  the  same  elementary 
atom  seems  to  vary  with  variations  in  the  actual  valency  of 
that  atom,  and  also  with  variations  in  the  chemical  type  of 
the  compounds  examined. 

159  The  rates  of  flow  through  capillary  tubes  of  liquid  com- 
pounds have  been  measured  by  several  observers,  especially  by 
Graham3  and  by  Pribram  and  Handl4.     The  results  obtained 
are  sufficient  to  establish  the  fact  of  a  connexion  between  the 
transpiration-rates  and  the    chemical    constitution    of  liquid 
carbon   compounds.     But  they  do  not    elucidate  the  exact 
nature  of  this  connexion.     Ostwald5  suggests  that  measure- 
ments should  be  made  at  the  boiling  points  of  various  liquids, 
as  some  of  the  results  obtained  by  Pribram  and  Handl  sug- 
gest that  the  transpiration-rates  of  equal  weights  of  analo- 
gous compounds  under  these  conditions  would  be  found  to  be 
nearly  proportional    to   the  molecular  weights  of  the  com- 
pounds. 

160  The  facts  of  electrolysis  have  been  used  as  arguments  in 
discussing   the    constitution    of    chemical    compounds ;    but 
the  questions  on   which  electrolytic  data  throw  light  rather 
belong  to  the  domain  of  chemical  kinetics  than  to  that  of 
statics6. 


.     l  Pogg.  Ann.  121.  55. 

a  Aririalen,Z2Z.  47 ;  Gazetta,  14.  368  (abstracts  in  C-  S.  Journal,  Abstracts  for 
1884.  808,  and  1885.  717.) 

3  Phil.  Trans.  1861.  373. 

4  Sitzungsberichte  der  K.  K,  Acad.  zu   Wien,  1878  (June  part);  1879  (June 
part). 

6  Lehrbuch,  1.  507. 

8  See  Book  n.  chap.  in. 


CH.  IV.  §§159,  1 60]  ELECTROLYSIS.  337 

Faraday's  laws  of  electrolysis,  translated  into  modern 
chemical  language,  assert  that  the  parts  or  ions  into  which  a 
compound  is  separated  by  electrolysis  are  chemically  equi- 
valent and  carry  with  them  equal  quantities  of  electricity. 

Electrolytes  belong  to  the  type  of  salts,  using  the  term 
in  its  widest  meaning.  Metallic  salts  are  generally  good  con- 
ductors when  molten,  and  they  readily  undergo  electrolysis. 
But  most,  if  not  all,  single  liquid  compounds, — e.g.  water, 
alcohol,  ether, — are  nearly  dielectrics.  Aqueous  solutions  of 
most  salts  are  electrolytes ;  and  the  nature  of  the  electrolytic 
decomposition  is  clearly  connected  with  the  quantity  of  the 
solvent.  Hence  it  is  probable  that  a  chemical  action  of  some 
kind  occurs  between  the  salt  and  the  water;  and  the  true 
electrolyte  may  be  a  molecular  aggregate,  or  aggregates, 
formed  by  the  union  of  the  two  kinds  of  molecules.  This 
view  is  confirmed,  on  the  whole,  by  the  electrolytic  behaviour 
of  many  double  salts,  some  of  which  are  decomposed  by  the 
current  in  the  same  way  as  a  mixture  of  their  constituents, 
while  others  give  distinctive  products.  The  behaviour  of  con- 
centrated aqueous  solutions  of  cadmium  iodide  and  chloride 
points  to  the  existence  and  electrolytic  decomposition  of 
aggregates,  probably  Cd3X6,  in  these  solutions,  while  the  be- 
haviour of  dilute  solutions  of  the  same  salts  is  explained  by 
supposing  that  the  body  undergoing  electrolysis  is  the  ordi- 
nary molecule  CdX2.  Whatever  be  the  exact  nature  of  the 
connexion  between  the  passage  of  the  current  through  a 
solution  of  a  salt  and  the  electrolysis  of  the  salt,  there  can  be 
little  doubt  that  the  process  is  intimately  conditioned  by  the 
nature  and  amount  of  the  solvent;  and  the  most  probable 
explanation  of  this  conditioning  effect  is  that  which  assumes 
the  formation  of  more  or  less  unstable  compounds  of  the 
solvent  with  the  dissolved  body. 

But  considerations  such  as  these  are  evidently  better  dis- 
cussed when  we  are  treating  the  subject  of  chemical  change, 
than  when  we  are  dealing  with  chemical  composition1. 


1  See  Book  11.  chap.  III.     The  student  would  do  well  to  read  the  chapter  on 
Electrolysis  in  Ostwald's  Lehrbuch  1.  533 — 568. 

M.  C.  22 


338  PHYSICAL  METHODS. 

Concluding  Remarks  on  Part  I. 

161  The  general  aim  of  the  first  part  of  this  book  has  been  to 
give  a  fairly  complete  account  of  the  present  state  of  know- 
ledge regarding  the  questions  of  chemical  statics,  indicating 
where  such  knowledge  requires  to  be  chiefly  supplemented, 
or  rendered  more  precise,  by  new  experimental  researches. 

I  have  regarded  those  questions  which  are  concerned  with 
substances,  or  systems  of  substances,  in  equilibrium  as  broadly 
belonging  to  chemical  statics ;  but  I  have  been  obliged  to 
pay  more  or  less  attention  to  the  kinetical  aspects  presented 
by  all  such  questions. 

It  may  be  said  that  the  fundamental  conception  of  atom 
and  molecule,  stated  and  illustrated  in  chapter  I.,  has  been 
regarded  in  its  applications  to  explain  resemblances  and 
differences  between  physical  and  chemical  phenomena,  nascent 
actions,  allotropy,  isomerism,  and  the  classification  of  elements 
and  compounds;  and  that  the  principal  methods,  both  purely 
chemical  and  chemico-physical,  which  are  employed  in  ex- 
amining these  problems,  have  been  sketched,  and  their  appli- 
cations illustrated. 

A  way  has  thus  been  cleared  by  which  we  may  hope  to 
approach  the  more  difficult  problems  of  chemical  kinetics. 


BK.II.  CH.I.§  162] 


BOOK    II. 
CHEMICAL   KINETICS. 

CHAPTER   I. 

THE   LAW   OF   MASS-ACTION. 


34O  THE   LAW  OF  MASS-ACTION.  [BOOK  II. 

regarded  now  from  the  statical  and  now  from  the  kinetical 
point  of  view. 

A  complete  account  of  any  chemical  change  must  include 
the  statement  of  the  relations  between  the  reacting  bodies, 
and  also  of  the  relations  between  the  forces  concerned  in  the 
change. 

163  The  question  of  chemical  kinetics  is :  what  is  the  cause  of 
chemical  change  ?     The  answer  to  this  question  has  always 
been  the  same :    the  cause  of  chemical  change  is  chemical 
affinity1. 

To  trace  the  history  of  the  term  cliemical  affinity,  and  to 
find  a  definite  and  quantitative  meaning  for  this  term,  is  to 
give  a  complete  account  of  chemical  kinetics. 

The  word  affinity  suggests  the  notion  of  kinship  or 
relationship ;  it  embodies  the  conception  of  the  earliest 
chemists  that  those  bodies  which  are  ready  to  enter  into 
union  are  akin  to  one  another.  In  the  sixteenth  and  seven- 
teenth centuries  the  notion  of  kinship  was  so  far  modified 
that  chemical  processes  were  regarded  as  caused  by  the 
mutual  attractions  of  bodies.  After  Newton  had  demon- 
strated the  law  of  gravitation,  the  conception  of  one  body 
attracting  another  with  a  force  varying  according  to  the 
masses  of  the  bodies  and  their  distances  apart  was  adopted 
in  chemistry,  and  was  developed  until  it  culminated  in  the 
tables  of  affinity  drawn  up  by  Bergmann  in  the  latter  part  of 
the  eighteenth  century. 

164  Bergmann  thought  that  the  cause  of  chemical  combina- 
tion was    identical  with  the  cause  of  gravitative  attraction ; 
but  he  said  that  the  results  differed   according  as   the   at- 
traction was  manifested  between  masses  or  between  minute 
particles  of  bodies.     In  the  latter  cases  the  attraction  was  the 
greater  the  nearer  were  the  particles  ;  hence,  said  Bergmann, 
chemical  action  occurs  more  readily  between  liquids  or  gases 
than  between  solids. 

1  I  have  closely  followed  Ostwald  (Lehrbuch  der  Allgemeinen  Chemie]  in 
dealing  with  the  subject  of  chemical  affinity.  The  second  volume  of  Ostwald's 
Lehrbuch  is  devoted  to  this  subject.  Without  the  help  of  this  book  I  could  not 
have  given  a  clear  account  of  affinity. 


CH.  i.  §§  163, 164]    BERGMANN'S  TABLES  OF  AFFINITIES.    341 

Bergmann  taught  that  the  result  of  the  chemical  at- 
traction, or  affinity,  between  two  bodies  is  to  cause  a  change 
wholly  in  the  direction  of  the  stronger  attraction,  unless  this 
should  be  reversed  by  the  more  powerful  attractive  force  of 
heat.  Thus,  suppose  that  two  bodies,  A  and  BC,  are  brought 
into  conditions  such  that  chemical  action  is  possible;  if  the 
attraction,  or  affinity,  of  A  for  B  is  greater  than  that  of  B  for 
C,  then  BC  will  be  decomposed  and  the  only  products  of  the 
change  will  be  the  new  bodies  AB  and  C ;  but  if  the  at- 
traction, or  affinity,  of  B  for  C  is  greater  than  that  of  B  for  A, 
no  chemical  change  will  occur. 

By  applying  this  conception  experimentally  Bergmann 
was  able  to  determine  the  order  of  the  affinities  of  series  of 
bodies.  Thus,  it  was  required  to  determine  the  order  of  the 
affinities  of  three  bodies,  A,  B  and  C,  towards  the  body  D. 
A  compound  AD  was  formed  and  this  was  caused  to  interact 
with  B  and  C,  respectively ;  if  AD  was  decomposed  by  B 
forming  BD  and  A,  then  the  affinity  of  B  for  D  was  said  to 
be  greater  than  that  of  A  for  D ;  if  AD  was  decomposed  by 
C  forming  CD  and  A,  and  if  BD  was  also  decomposed  by  C 
forming  CD  and  B,  then  C  was  said  to  have  a  greater  affinity 
for  D  than  either  A  or  B.  These  results  were  then  tabulated 
in  a  table  of  affinity  as  follows  : — 

Order  of  affinities  towards  D. 

C 

B 

A. 

But  it  was  frequently  found  that  a  body  which  had  no  action 
on  another  when  the  two  were  mixed  in  solution  at  the 
ordinary  temperature  would  decompose  that  other  when  the 
two  were  fused  together  at  a  high  temperature.  Hence 
Bergmann  found  it  necessary  to  perform  a  vast  number  of 
experiments,  and  to  draw  up  at. least  two  tables  of  affinity  for 
each  substance,  one  shewing  its  affinities  at  ordinary  tem- 
peratures in  solution,  and  the  other  shewing  its  affinities 
at  high  temperatures  when  fused  with  other  substances. 
Bergman n's  table  for  potash,  for  instance,  was  constructed 
thus :— 


342  THE   LAW   OF   MASS-ACTION.  [BOOK  II. 

ORDER  OF  AFFINITIES  FOR  POTASH. 

Wet  way  (ord.  temp.).  Dry  way  (high  temp.). 
Sulphuric     acid  Phosphoric    acid. 

Nitric  „  Boric  „ 

Hydrochloric  „  Arsenic  „ 

Phosphoric      „  Sulphui'ic         „ 

Arsenic  „  Nitric  „ 

Acetic  „  Hydrochloric  „ 

&c.        &c.  &c.  „ 

This  table  conveyed  the  information  that  a  solution  of 
a  compound  of  potash  with  any  acid  in  the  left-hand 
column  would  be  decomposed  by  a  solution  of  any  acid 
placed  in  the  same  column  above  the  acid  which  was  com- 
bined with  potash ;  and  that  a  solid  composed  of  potash  with 
any  acid  in  the  right-hand  column  would  be  decomposed  by 
heating  with  any  acid  placed  in  the  same  column  above  the 
acid  which  was  combined  with  potash. 

In  Bergmann's  view,  affinity  acted  in  one  direction  only. 
165        The  publication   by  Berthollet  in   1803  of  the  Essai  de 
Statique  Chitnique  marked  the  next  great  step  in  advance  in 
the  study  of  affinity. 

Berthollet,  like  Bergmann,  regarded  chemical  action  as 
the  result  of  attractions  between  the  small  particles  of  bodies. 
When  conditions  are  favourable,  this  attraction  results,  ac- 
cording to  Berthollet,  first  in  cohesion  and  then  in  combina- 
tion. But  other  forces  may  come  into  play  which  are  opposed 
to  the  attraction  called  affinity;  heat  may  cause  the  ex- 
pansion of  substances  which  would  otherwise  combine ; 
solution  may  weaken,  or  destroy,  the  cohesion  of  the 
.  particles  of  a  solid.  Whether  combination  occur  or  not,  and 
if  it  occur,  whether  the  products  remain  unchanged  or  not, 
depends,  on  Berthollet's  view,  upon  the  relative  magnitudes  of 
the  opposing  forces.  If  the  attraction  between  the  particles 
of  different  kinds  of  matter  is  greater  than  the  action  of  the 
forces  which  tend  to  separate  these  particles,  then  a  new 
compound  or  compounds  will  be  formed.  Should  these 
compounds  be  solids  under  the  experimental  conditions,  the 
cohesion  of  their  particles  will  act  in  the  same  direction  as 
the  attraction  of  affinity  which  is  the  immediate  agent  in 


CH.  i.  §165]    BERTHOLLET'S  WORK  ON  AFFINITY.  343 

their  production.  The  final  arrangement  of  the  particles  of 
two  kinds  of  matter  depends,  according  to  Berthollet,  not 
only  on  the  relative  magnitudes  of  the  different  attractions 
between  them,  but  also  on  the  relative  masses  of  the  re- 
acting bodies ;  thus,  a  relatively  small  attraction  may  be  made 
to  overcome  a  greater,  by  largely  increasing  the  mass  of  one 
of  the  two  kinds  of  matter. 

Berthollet  regarded  a  liquid  holding  a  solid  in  solution  as 
a  system  in  a  state  of  more  or  less  unstable  equilibrium ;  by 
removing  some  of  the  liquid  by  evaporation,  or  by  lowering 
the  temperature,  or  in  other  ways,  this  equilibrium  might  be 
overthrown,  and  crystals  might  separate  containing  particles 
both  of  the  solid  previously  in  solution  and  also  of  water 
changed  from  the  liquid  to  the  solid  state.  Such  a  system, 
said  Berthollet,  will  present  two  extreme  cases  ;  in  one  case 
all  the  solid  is  held  in  solution  by  the  liquid,  and  in  the  other 
all  the  liquid  is  changed  to  the  state  of  solid.  Between  these 
extremes  there  may  be  many  states  each  marked  by  a  certain 
definite  relation  between  the  amounts  of  solid  and  liquid 
compounds ;  for  Berthollet  regarded  the  solution,  no  less  than 
the  crystals  which  separated,  as  a  compound,  or  a  series  of 
compounds,  of  water  and  salt. 

Combination  and  solution  were  looked  on  by  Berthollet 
as  analogous  actions.  He  said 

"  In  solution,  one  pays  attention  chiefly  to  the  liquidity  acquired  by 
the  solid  by  combining  [with  the  solvent],  and  especially  to  the  uniformity 
of  the  parts  of  the  liquid  compound.... In  a  combination  one  principally 
considers  the  other  properties  of  the  compound  which  is  produced, 
comparing  therewith  the  properties  of  the  substances  which  produced  it. 
In  most  cases  solution  is  due  to  a  combination  so  feeble  that  the 
properties  of  the  dissolved  substance  do  not  disappear".1 

Again ; 

"  Chemical  action  is  reciprocal ;  its  effect  is  the  result  of  a  mutual 
tendency  to  combination.  One  ought  not,  strictly  speaking,  to  say  that 
a  liquid  acts  upon  a  solid,  rather  than  that  the  solid  acts  upon  the  liquid ; 
it  is  more  convenient  however  to  ascribe  the  whole  of  the  action  to  one 
of  the  substances,  when  one  wishes  to  examine  the  products  of  the  action, 
rather  than  the  action  itself."  * 

1  Essai,  1.  59—60.  a  Essai,  1.  36—37. 


344  THE  LAW  OF  MASS-ACTION.  [BOOK  II. 

When  lime  is  placed  in  water,  mutual  action,  said  Berthollet, 
begins  at  once,  but  the  cohesion  of  the  particles  of  the  solid 
is  so  great  that  the  dissolving  action  of  the  water  does  not 
produce  any  marked  effect  for  some  time ;  but  water  is  being 
absorbed  by  the  lime,  and  thus  the  effect  of  the  cohesion  of 
the  particles  of  the  lime  is  slowly  overcome  by  that  of  the 
solvent  action  of  the  water,  until  finally  the  lime  dissolves. 
During  this  process  two  combinations  of  lime  and  water  are 
formed,  one  solid,  the  other  liquid ;  the  effect  of  one  force, 
cohesion,  is  to  increase  the  amount  of  the  former ;  the  effect 
of  another  force,  solution,  is  to  increase  the  amount  of  the 
latter  combination.  A  state  of  equilibrium  is  established, 
and  continues  so  long  as  the  conditions  are  unchanged ; 
but  alteration  of  temperature,  or  changes  in  the  relative 
masses  of  water  and  lime,  suffice  to  overthrow  this  equilibrium 
and  to  establish  another1. 

Berthollet  not  only  formed  a  clear  mental  image  of  a 
system  as  held  in  equilibrium  by  the  actions  and  reactions  of 
its  various  constituents,  but  he  had  also  what  I  think  must  be 
regarded  as  a  very  clear  conception  of  the  chief  forces  con- 
cerned in  maintaining  this  equilibrium.  In  the  summary  to 
Part  I.  of  the  Essai,  he  says : 

"The  chemical  qualities  of  different  substances  depend  (i)  on  their 
tendencies  to  combine,  whereby  they  mutually  saturate  each  other,  and 
which  tendencies  remain  more  or  less  dominant  in  the  compounds 
produced ;  (2)  on  their  relations  to  heat,  which  modify  their  combining 
powers,  by  causing  variations  in  the  quantities  of  the  substances  coming 
within  the  spheres  of  mutual  action,  and  also  by  opposing  elasticity 
(elasticite'*'}  to  condensation,  the  latter  of  which  is  one  of  the  effects  of 
combination ;  (3)  on  the  mutual  actions  of  their  small  particles  (molecules*), 
acting  in  the  same  direction  as  the  affinity  which  has  produced  com- 
bination, but  opposed  to  actions  and  reactions  between  these  particles 
and  those  of  other  substances ;  (4)  on  their  relations  to  other  substances, 
which  combine  with  them,  but  not  so  as  to  produce  a  mutual  saturation 

1  Essai,  1.  37. 

3  Elasticity  Berthollet  uses  this  word  as  meaning  nearly  the  same  as  dilata- 
tion, or  perhaps  we  might  now  say  disgregation. 

3  Molecules.  This  word  as  employed  by  Berthollet  means  only  a  small  particle ; 
I  have  thought  it  better  not  to  use  the  term  molecule,  as  this  is  now  employed  with 
a  more  definite  meaning  than  small  particle. 


CH.  I.§l66]         BERTHOLLET   AND   BERGMANN.  345 

(saturation^},  but  rather  a  division  and  varying  distribution  of  properties, 
and  chiefly  of  those  properties  which  depend  on  the  constitution  (con- 
stitution}?* 

L66  Berthollet's  conception  of  affinity  as  an  attractive  force 
acting  between  the  minute  particles  of  bodies,  and  modified 
in  its  results  by  the  action  of  other  forces,  led  him  to  pay 
great  attention  to  the  influence  of  the  masses  of  the  bodies 
taking  part  in  any  chemical  change.  Just  as  the  cohesion, 
and  elasticity,  &c.,  of  the  members  of  a  system  of  bodies  are 
dependent,  among  other  conditions,  on  the  masses  of  the 
bodies,  so,  in  Berthollet's  view,  is  affinity  dependent  on  mass : 

"  Every  substance,"  said  Berthollet,  "  which  enters  into  combination 
reacts  by  its  affinity  and  its  mass."3 

The  conception  which  the  great  French  chemist  formed  of  a 
chemical  reaction  was  radically  opposed  to  that  upheld  by 
his  illustrious  Swedish  predecessor. 

Let  two  acids  interact  with  a  base  in  aqueous  solution. 
Bergmann  asserted  that  the  acid  with  the  stronger  affinity 
combined  with  the  whole  of  the  base,  and  the  other  acid 
remained  uncombined.  Berthollet  declared  that  both  acids 
interacted  with  the  base,  and  that  the  mass  of  the  base  which 
remained  combined  with  either  acid  when  equilibrium  was 
established  depended  partly  on  the  intensity  of  the  attraction 
between  the  particles  of  the  base  and  of  the  acids,  and  partly 
on  the  relative  masses  of  the  three  bodies  present  in  the 
reacting  system. 

Bergmann  taught  that  a  chemical  change  proceeds  in  one 
direction  only,  and  that  the  direction  is  entirely  dependent  on 
the  relative  affinities  of  the  interacting  bodies;  but  he  was 
obliged  to  acknowledge  that  the  affinities  of  some  bodies  for 

1  Saturation.     By  saturation  of  properties  Berthollet  means  that  merging  of 
the  properties  of  the  constituents  in  those  of  the  new  compound  which  is  so 
characteristic  of  chemical  change. 

2  Constitution.     The  constitution  of  a  substance  is  conditioned  according  to 
Berthollet  by  its  condensation  and  dilatation :  '  the  properties  which  depend  on 
the  constitution'  of  a  substance  may  be  taken  as  meaning,  broadly,  the  physical 
properties  of  the  substance. 

3  £ssai,  1.  2. 


346  THE  LAW  OF   MASS-ACTION.  [BOOK  II. 

another  are  sometimes  so  nearly  balanced  that  a  compound 
of  all  the  reacting  bodies  is  produced ;  and  he  was  also  forced 
to  admit  that  the  order  of  the  affinities  of  a  series  of  bodies 
for  one  and  the  same  body  may  be  changed  or  even  reversed 
by  changing  the  physical  conditions  under  which  the  chemical 
reaction  proceeds. 

Berthollet,  on  the  other  hand,  taught  that  a  chemical 
change  may,  and  often  does,  proceed  in  two  directions ;  that 
is  to  say,  that  certain  bodies  may  react  to  produce  others 
which  may  then  by  their  interactions  reproduce  the  original 
bodies ;  that  the  equilibrium  which  is  finally  attained  by  a 
system  of  interacting  bodies  is  the  result  of  the  action  and 
reaction  of  all  the  members  of  the  system;  and  that  the 
conditions  which  chiefly  affect  this  equilibrium  are  the  affinity 
and  the  mass  of  each  body,  and  also  the  physical  conditions 
under  which  the  change  proceeds  and  the  physical  properties 
of  the  different  possible  products  of  the  change. 

Berthollet's  researches  established  three  points  of  funda- 
mental importance : — chemical  action  is  conditioned  not  only 
by  the  intensities  of  the  affinities,  but  also  by  the  relative 
masses,  of  the  reacting  bodies ;  a  chemical  change  is  gene- 
rally more  or  less  reversible  by  changing  the  masses  of  the 
reacting  bodies,  it  is  only,  in  extreme  cases  that  a  chemical 
change  proceeds  wholly  in  one  direction ;  the  forces  which 
come  into  play  in  chemical  occurrences  are  of  the  same  kind 
as  those  which  we  call  physical. 

167  The  period  of  sixty  years  following  the  publication  of 
Berthollet's  Essai  is  not  marked  by  any  great  advance  in  the 
study  of  chemical  affinity ;  nevertheless  various  important 
researches  were  conducted  in  this  period  the  results  of  which 
served  to  emphasize  the  importance  of  Berthollet's  funda- 
mental conception  of  the  influence  of  the  relative  masses  of 
chemically  reacting  bodies  on  the  course  of  a  chemical 
change  and  on  the  equilibrium  finally  attained  by  the  system. 

In  1853  Bunsen1  examined  the  change  which  occurs  when 
a  mixture  of  carbon  monoxide  and  hydrogen  is  exploded 
with  a  quantity  of  oxygen  less  than  sufficient  for  the  com- 

1  Annalen,  85.  131 ;  see  also  Horstmann,  Amialen,  190.  238. 


CH.  I.  §§  167,  1  68]      WORK  OF  GULDBERG  AND  WAAGE.  347 

plete  combustion  of  both  gases.  Bunsen  shewed  that  some  of 
the  oxygen  enters  into  combination  with  the  carbon  mo- 
noxide and  some  with  the  hydrogen,  and  that  the  quantity  of 
each  of  these  gases  burnt  depends  on  the  relative  masses  of 
the  combustible  gas  and  the  oxygen. 

In  1855,  Gladstone1,  by  studying  the  amount  of  change 
which  occurs  when  potassium  sulphocyanide  and  ferric 
chloride  react  in  aqueous  solution,  exhibited  very  clearly  the 
influence  of  mass  on  chemical  change.  Gladstone  shewed 
that  when  ferric  chloride  and  potassium  sulphocyanide  react, 
only  a  portion  of  each  salt  is  changed  unless  the  mass  of  one 
is  made  600  or  700  times  as  great  as  that  of  the  other  ;  he 
also  shewed  that  the  quantity  of  ferric  sulphocyanide  formed 
increases  continuously  with  an  increase  in  the  quantity  of 
potassium  sulphocyanide  used. 

It  is  important  to  note  that  Gladstone  used  determina- 
tions of  physical  properties,  such  as  depth  of  colour,  as  in- 
dications and  measurements  of  the  chemical  change  which 
occurred. 

Berthollet  and  P.  de  Saint  Gilles2  in  1862—63  made  a 
large  number  of  measurements  of  the  amount  of  change 
which  occurs  when  an  alcohol  and  an  acid  react  to  form  an 
ethereal  salt  and  water,  and  established  the  influence  of  the 
masses  of  the  reacting  bodies  on  the  change  in  question. 
168  The  year  1867  is  marked  in  the  history  of  chemistry  by 
the  publication  of  a  most  important  memoir  on  affinity  by 
Guldberg  and  Waage  entitled  Etudes  sur  les  Affinitts  Chimi- 


Guldberg  and  Waage  restate  Berthollet^  law  of  mass- 
action  in  a  form  in  which  it  is  capable  of  quantitative  ap- 
plication ;  they  assert  that 

1  Phil.  Trans.  1855.  179;  and  C.  S.  Journal,  9.  54. 

2  Ann.  Chim.  Phys.  (3).  65.  385;  66.  5;  68.  225.     Among  other  memoirs  on 
the  influence  of  mass  may  be  mentioned  Margueritte  Compt.  rend.  38.  304  ;  Tissier, 
Cotnpt.  rend.  41.  312;  Dulong,  Ann.   Chim.  Phys.  82.  275;  Rose,  Pogg.  Ann. 
94.  481;  95.  96,  284,  426;  Malaguti,  Ann.  Chim.  Phys.      (3).  37.    198;    Chic- 
zynski,  Annalen,  Supplbd.  4.  226;  Morris,  Annalen,  213.  253. 

3  Published  by  the  University  of  Christiania  ;   continuation  in  J.  fiir  praki. 
Chemie  (2).  19.  69. 


34$  THE   LAW   OF   MASS-ACTION.  [BOOK  II. 

Chemical  action  is  proportional  to  the  active  mass  of  each  of 
the  bodies  taking  part  in  the  reaction. 

The  active  mass  of  a  specified  body  taking  part  in  a 
reaction  is  the  mass  of  that  body  stated  in  equivalent 
weights,  present  in  unit  volume  of  the  chemical  system.  Thus 
if  solutions  of  hydrochloric  acid,  sulphuric  acid,  and  caustic 
soda  are  mixed  in  the  ratio  2HC1:  H2SO4:  2NaOH,  the 
active  masses  of  the  hydrochloric  acid,  sulphuric  acid,  and 
soda  are  I,  I,  and  I,  respectively,  H2SO4  being  taken  as  one 
equivalent  of  sulphuric  acid. 

Guldberg  and  Waage's  law  of  mass-action  states  that  the 
action  of  each  substance  in  a  system  of  interacting  bodies  is 
proportional  to  the  active  mass  of  that  substance,  and  that 
the  total  action  is  proportional  to  the  product  of  all  the  active 
masses. 

But  the  amount  of  chemical  change  which  occurs  when 
two  or  more  substances  react  is  not  dependent  solely  on  the 
active  masses  of  the  substances,  it  is  also  conditioned  by  the 
chemical  nature,  and  the  state  of  aggregation,  of  the  sub- 
stances, the  temperature,  and  other  variables.  Guldberg  and 
Waage  group  together  these  variables  and  express  them  by 
a  coefficient  called  by  them  the  coefficient  of  affinity,  and 
represented  by  the  symbol  k. 

Let  two  substances  P  and  Q  react,  and  let  the  active 
masses  of  these  be  represented  by  the  symbols  /  and  q ; 
further  let  the  coefficient  of  affinity  for  the  reaction  between 
P  and  Q  be  represented  by  k ;  then  the  amount  of  chemical 
change  which  occurs  will  be  proportional  to  the  product 
k.  p.  q.  Let  the  products  of  the  interaction  of  P  and  Q  be 
two  new  bodies  P'  and  Q,  and  let  the  active  masses  of  these 
bodies  be  represented  by  the  symbols  /'  and  q,  and  the 
coefficient  of  affinity  for  the  reaction  between  P'  and  Q'  be 
represented  by  k',  then  the  amount  of  chemical  change  which 
occurs  between  P'  and  Q'  will  be  proportional  to  the  product 
k'.  /'.  q'.  Now  when  P  and  Q  interact  certain  quantities  of 
P'  and  Q'  will  be  formed,  and  these  will  at  once  interact  to 
re-form  P  and  Q ;  this  will  proceed  until  equilibrium  is 
established,  after  which  no  further  change  will  occur  in  the 


CH.  I.§l68]      WORK   OF  GULDBERG  AND  WAAGE.  349 

active  masses  of  the  various  bodies  nor  in  the  values  of  the 
coefficients  of  affinity  of  either  the  direct  or  the  reverse 
change.  When  equilibrium  is  attained  the  product  k.  p.  q, 
will  be  equal  to  the  product  k'.p'.  q .  Hence  the  conditions  of 
equilibrium  are  expressed  by  the  equation 

k.p.q.  =  k'.p'.q. 

But  as  the  reaction  between  P  and  Q  proceeds  the  active 
masses  of  these  bodies  will  be  decreased,  and  the  active 
masses  of  the  products  of  the  change,  P  and  Q',  will  be  in- 
creased. Let  P,  Q,  P',  and  Q  represent  the  masses  of  the 
four  bodies  present  in  the  chemical  system  at  the  beginning 
of  the  change,  these  masses  being  stated  in  equivalent 
weights ;  when  equilibrium  is  established  x  equivalents  of 
P  and  x  of  Q  will  disappear  and  x  equivalents  of  P  and 
x  equivalents  of  Q'  will  simultaneously  be  formed ;  let  /,  q, 
/',  and  q'  represent  the  active  masses  of  the  four  bodies 
present  when  equilibrium  results,  then  the  values  of  these 
active  masses  will  be  as  follows  : — 

P-x  Q-x       ,     P  +  x       ,     Q'+x 

p  = ,    q  =• ,  P  — >   Q  — » 

v  V        f          V  v 

where  v  =  the  total  volume  of  the  system,  taken  as  unity. 

By  substituting  the  values  for/,  q,p',  and  q'  in  the  equation 
of  equilibrium  we  have 

(P-x}(Q-x}=^  (P* +  *)«?+*). 

This  equation  holds  good  for  all  values  of  P,  Q,  P',  and  Q. 

k' 

The  ratio  -r  can  be  calculated  from  a  determination  of  x  for 
k 

one  special  case,  and  from  the  value  of  this  ratio  values  can 
be  found  for  x,  and  therefore  for  the  distribution  of  the  four 
reacting  bodies  when  equilibrium  results,  starting  with  any 
specified  quantities  of  P,  Q,  P/,  and  Q'. 

Guldberg  and  Waage  thus  put  Berthollet's  conception  of 
the  influence  of  mass  into  an  exact  form.  They  consider  the 
masses  of  the  several  bodies  comprising  a  chemical  system 
present  at  the  moment  when  equilibrium  is  established.  The 


350  THE   LAW   OF   MASS- ACTION.  [BOOK  II. 

attempts  made  to  formulate  the  influence  of  mass  on  chemical 
change  previous  to  the  work  of  the  Norwegian  naturalists 
had  been  implicitly  based  on  measurements  of  the  masses  of 
the  reacting  bodies  present  when  the  reaction  began. 
169  In  their  first  memoir  (Etudes  &c.)  Guldberg  and  Waage 
regard  the  occurrence  of  a  chemical  change  as  caused  by 
'  chemical  force ' ;  they  say  that  when  equilibrium  results  in  a 
system  of  four  bodies,  P,  Q,  P',  and  Q',  the  force  bringing 
about  the  formation  of  P'  and  Q'  is  held  in  equilibrium  by 
the  force  which  causes  the  re-formation  of  P  and  Q.  They 
also  attempt  to  take  into  account  the  possibility  of  secondary 
changes  among  the  reacting  bodies  and  to  express  these  in 
equations.  But  the  formulae  thus  arrived  at  are  too  com- 
plicated for  practical  application ;  and  moreover  the  con- 
ception of  chemical  force  is  vague  and  unsatisfactory. 

In  their  second  memoir1  Guldberg  and  Waage  follow  the 
example  of  van't  Hoff8,  and,  abandoning  the  notion  of 
chemical  force,  attempt  to  find  formulas  which  may  be 
applied  in  practice  by  starting  with  the  clear  conception  of 
chemical  equilibrium  being  dependent  on  the  equality  of  the 
rates  of  the  direct  and  reverse  chemical  changes ;  i.  e.  they 
consider  that  equilibrium  results  in  a  chemical  system  when 
the  quantity  of  substance  changed  in  one  direction  is  equal  to 
that  formed  in  the  other  direction  in  a  given  time.  Many 
measurements  had  been  made  of  the  rates  of  chemical  actions, 
but  Guldberg  and  Waage  were  the  first  to  establish  clearly 
the  connexion  between  the  velocity  of  a  chemical  change  and 
the  attainment  of  equilibrium  by  the  system.  This  was  done 
in  their  memoir  of  1867,  but  the  formulae  given  in  that 
memoir  are  complicated  and  scarcely  suited  for  accurate 
application.  The  equation  arrived  at  in  the  second  memoir 
as  representing  the  connexion  between  reaction-velocity  and 
equilibrium  is  identical  with  that  we  have  already  considered ; 
viz.  k.p.q  =  k'.p '.  q'. 

Let  there  then  be  a  chemical  system  of  four  bodies,  P,  Q, 
P",  and  Q';  let  P  and  Q  react  to  produce  P  and  Q',  and 
P'  and  Q'  react  to  re-produce  P  and  Q  ;  equilibrium  results 

1  J.furprakt.  Chemie,  (2).  19.  69.  2  Ber.  10.  669. 


CH.  I.  §§  169,  I/O]      WORK  OF  GULDBERG  AND  WAAGE.         351 

when  the  velocity  of  the  direct  change  (i.e.  the  production  of 
F  and  Q'}  is  equal  to  that  of  the  reverse  change  (i.e.  the 
production  of  P  and  Q).  The  conditions  of  equilibrium  are 
expressed  by  the  equation 

k.p.q.  =  k'.p'.q', 
or,  as  before, 


k' 
It  is  important  to  note  here  that  the  ratio  -r  is  not  analysed  ; 

it  is  simply  the  ratio  of  the  affinity  of  P  and  Q  to  that  of  the 
affinity  of  F  and  Q  ;  and  the  term  affinity  is  used  as  a  short 
expression  for  the  unknown  cause  of  the  chemical  reaction 
between  the  reacting  bodies. 

170  Guldberg  and  Waage  tested  their  equation  of  equilibrium 
both  by  using  the  results  obtained  by  other  chemists  and 
also  by  experiments  which  they  themselves  conducted. 

Thus  the  results  of  Berthollet  and  P.  de  Saint  Gilles1  on 
the  etherification  of  alcohols  by  reacting  with  organic  acids 
were  used  by  Guldberg  and  Waage.  The  members  of  the 
reacting  system  are  alcohol,  acid,  ethereal  salt,  and  water  ; 
the  direct  change  results  in  the  production  of  ethereal  salt 
and  water,  and  the  reverse  change  produces  alcohol  and  acid. 
The  following  numbers  shew  the  close  agreement  between 
the  observed  and  calculated  values  of  xt  i.e.  the  number  of 
equivalents  of  acid  or  alcohol  transformed  into  ethereal  salt 
and  water  when  equilibrium  is  established. 


SERIES  I. 

Q 

Observed. 

Calculated. 

One  equivalent  acid  + 

i 

•665 

•668 

Q  equivalents  alcohol. 

i  '5 

779 

772 

2 

•828 

•827 

2-8 

•856 

•870 

3 

•882 

•878 

12 

•932 

•930 

500 

I'OOO 

I  '000 

SERIES  II. 

P 

One  equivalent  alcohol  + 

I 

•665 

•668 

P  equivalents  acid. 

2 

•858 

•856 

5 

•966 

•972 

1  Ann.  Chim. 

Phys.  (3). 

68.  385. 

352  THE   LAW   OF   MASS-ACTION.  [BOOK  II. 


SERIES  III.  P  Observed.        Calculated. 

One  equiv.  acid  +  o  '665  '668 

one  equiv.  alcohol  +  0*13  '626  '648 

P  equivs.  ethyl  acetate.  0-85  '563  '550 

i'6  -521  -487 

SERIES  IV.  Q 

One  equiv.  acid+  o  '882  '871 

three  equivs.  alcohol  +  i  '809  '803 

Q  equivs.  water.  2  739  744 

8  -468  -512 

Guldberg  and  Waage  themselves  examined  the  reaction 
which  occurs  between  barium  sulphate  and  potassium  carbo- 
nate in  presence  of  water.  In  this  case  two  of  the  four 
members  of  the  system  are  insoluble,  viz.  barium  sulphate 
and  barium  carbonate.  Guldberg  and  Waage  shewed  that  if 
the  absolute  masses  of  the  insoluble  members  of  a  reacting 
system  are  fairly  large,  and  the  volume  of  the  liquid  is  kept 
constant,  the  changes  in  the  absolute  masses  of  the  insoluble 
bodies  do  not  appreciably  affect  the  active  masses  of  these 
bodies1;  and  this  result  was  fully  confirmed  by  Ostwald2. 

In  the  reaction  between  potassium  carbonate  (P}  and 
barium  sulphate  (Q)  producing  potassium  sulphate  (P'}  and 
barium  carbonate  (Q'),  let  the  active  mass  of  the  potassium 
carbonate  be  /,  that  of  the  barium  sulphate  q,  that  of  the 
potassium  sulphate  p\  and  that  of  the  barium  carbonate  q  ', 
then,  as  q  and  q'  are  constant,  the  equation  of  equilibrium 
becomes 


The  following  numbers  shew  how  closely  the  values  of 
x  calculated  for  the  condition  that  equilibrium  is  attained 
agree  with  the  observed  values  :  — 


SERIES  I.                                Q  Observed.         Calculated. 

I  equiv.  barium  sulphate+           3'5  719                       715 

500  equivs.  water  (at  1 00°)  +        2^5  "500                      '500 

Q  equivs.  potassium  carbonate    2  "395                      '391 

i  -176                     -178 

1  J.fiir prakt.  Chemie,  (2).  19.  469.  '*  J.fiir  prakt.  Chemie,  (2).  22.  256. 


CH.  I.  §§  170,171]   WORK  OF  GULDBERG  AND  WAAGE.  353 

SERIES  II.  Q  Q  Observed.  Calculated. 

i  equiv.  barium  sulphate  4-  2  '25  -20  -198 

500  equivs.  water  (at  ioo°)+  3  "25  '408  '409 

<2  equivs.  potassium  carbonate  +  2  -50  trace  -coo 
Q  equivs.  potassium  sulphate. 

171  Experimental  evidence  in  favour  of  Guldberg  and  Waage's 
law  of  mass-action  has  been  obtained  by  various  observers 
using  different  methods.  One  of  the  great  difficulties  consists 
in  finding  suitable  methods  for  measuring  the  distribution  of 
the  members  of  a  reacting  system  all  of  which  remain  in 
solution  when  equilibrium  is  established.  Very  many  of  the 
methods  which  have  been  found  to  give  trustworthy  results 
are  based  on  the  same  principle,  which  is  that  the  amount  of 
chemical  change  in  a  homogeneous  system  is  deducible  from 
measurements  of  some  definite  physical  property  of  the 
system  and  determinations  of  the  changes  in  the  value  of 
this  property. 

Thomsen1,  in  1869  and  subsequent  years,  shewed  that 
when  two  acids  and  a  base  react  in  aqueous  solution,  the 
distribution  of  the  base  between  the  acids  can  be  determined 
by  thermo-chemical  methods.  Let  the  heat  of  neutralisation 
of  the  acid  A  by  the  given  base  be  x  gram-units,  and  let  the 
heat  of  neutralisation  of  the  other  acid  B  by  the  same  base  be 
y  gram-units  ;  then  if  both  acids  simultaneously  react  with 
the  base  the  quantity  of  heat  produced  may  be  x  units,  in 
which  case  the  whole  of  the  base  has  combined  with  the 
acid  A,  or  y  units,  in  which  case  the  whole  of  the  base  has 
combined  with  the  acid  B,  or  a  number  between  x  and  yt  in 
which  case  the  base  has  divided  itself  between  the  two  acids  ; 
in  the  last  case  the  proportion  of  base  which  has  combined 
with  each  acid  may  be  calculated  from  the  observed  thermal 
value  of  the  reaction2. 

In  1876  Ostwald3  shewed  that  the  distribution  of  a  base 
between  two  acids  can  be  determined  from  measurements  of 
the  specific  volume  of  a  solution  of  each  acid,  of  the  base,  of 
the  liquid  formed  by  mixing  each  acid  separately  with  the 
base,  and  of  the  liquid  formed  by  mixing  both  acids  simul- 

1  Pogg.  Ann.  138.  65.  2  See  post  par.  183. 

3  P°SS-  Ann.  Ergzbd.  8.  154. 
M.  C.  23 


354  THE   LAW  OF   MASS-ACTION.  [BOOK  II. 

taneously  with  the  base1.  The  results  'obtained  by  Thomsen 
and  by  Ostwald  have  fully  confirmed  the  law  of  mass-action 
enunciated  by  Guldberg  and  Waage  ;  and  this  law  has  also 
been  upheld  by  other  series  of  experiments  conducted  by 
various  chemists2. 

The  law  of  mass-action  may  then  be  regarded  as  well- 
established  ;  this  law  asserts  that  the  amount  of  chemical 
change  which  occurs  when  a  system  of  interacting  bodies 
attains  equilibrium  is  proportional  to  the  product  of  the 
active  masses  of  all  the  bodies  taking  part  in  the  change  and 
the  coefficient  of  affinity  of  the  change. 

1  See  post  par.  184. 

2  These  experiments  will  be  described  in  some  detail  later;  see  pars.  185,  186. 


CHAPTER   II. 

CHEMICAL  DYNAMICS. 

72  A  DETAILED  examination  of  the  applications  of  the  law 
of  mass-action,  which  was  stated  and  briefly  illustrated  in 
Chap.  I.,  leads  to  the  consideration  of  the  forces  which  come 
into  play  in  chemical  changes1. 

As  forces  are  measured  in  dynamics  either  by  measuring 
the  velocity  produced  in  a  specified  mass  in  unit  of  time,  or 
by  opposing  the  unknown  force  by  another  of  known  amount 
until  equilibrium  is  attained,  so  may  measurements  of  chemical 
forces  be  obtained  by  determining  the  amount  of  change 
which  occurs  in  unit  of  time,  or  by  opposing  the  direct  change 
by  another  in  the  opposite  direction  and  determining  the 
conditions  of  equilibrium. 

It  is  important  to  notice  that  when  we  speak  of  chemical 
force  the  term  force  is  used  with  a  meaning  different  from 
that  in  which  it  is  employed  in  dynamics  :  by  chemical  force 
we  mean  the  product  of  the  active  masses  of  the  various  bodies 
comprising  the  changing  system  and  the  constant  of  velocity  of 
the  change.  And  by  velocity  we  mean,  not  the  ratio  of  space 
traversed  to  time  used  as  in  dynamics,  but  the  ratio  of 
material  chemically  changed  to  time  used  in  the  change. 

Using  the  term  chemical  force  with  this  meaning,  we 
shall  find  that  a  chemical  change  is  conditioned  by  changes 
in  the  chemical  force  in  much  the  same  way  as  an  electric 
current  is  conditioned  by  changes  of  potential. 

1  In  this  Chapter  I  have  again  closely  followed  Ostwald's  Lehrbuch  der 
Allgemeinen  Chemie,  Bd.  II.  The  present  chapter  is  a  condensed  account  of 
the  greater  part  of  the  second  book  of  Ostwald's  Verwandtschaftslehre. 

23—2 


356  VELOCITY  OF  CHEMICAL  CHANGE.  [BOOK  II. 

Those  methods  of  measuring  what  we  have  called  chemical 
forces  which  are  based  on  determinations  of  the  velocities  of 
chemical  changes  may  be  called  kinetical  methods,  while  the 
term  statical  methods  may  be  applied  to  those  which  are 
founded  on  determinations  of  the  conditions  of  equilibrium. 

The  methods  whereby  measurements  have  been  made  of 
the  velocities  of  chemical  changes,  with  the  view  of  de- 
termining the  intensities  of  the  chemical  forces,  have  usually 
been  chemical ;  whereas  both  physical  and  chemical  methods 
have  been  used  for  determining  the  conditions  of  equilibrium 
of  chemical  systems. 

I  shall  begin  by  considering  some  of  the  kinetical 
methods. 

SECTION  I.      Velocity  of  Chemical  CJiange. 

173  Wenzel1,  in  17/7,  measured  the  times  required  by  different 
acids  to  dissolve  equal  quantities  of  the  same  metal,  and  he 
attempted    to   draw  inferences    from    the   results   as   to   the 
relative  affinities  of  the  acids.     Thus,  he  says  : — 

"  If  an  acid  dissolves  one  drachma  of  copper  or  zinc  in  an  hour,  then 
an  acid  of  half  the  strength  requires  two  hours  to  dissolve  the  same 
amount  of  copper  or  zinc,  the  surfaces  exposed  and  the  temperature  being 
constant." 

Berthollet2  made  observations  somewhat  similar  to  those 
of  Wenzel.  He  said  that  the  velocity  of  a  chemical  change 
is  greater  the  greater  is  the  chemical  force ;  but  he  noticed 
that  the  velocity  diminishes  as  the  change  approaches  com- 
pletion, and  that  reactions  which  begin  rapidly  often  finish 
very  slowly. 

174  Wilhelmy8,  in   1850,  gave   a   mathematical  form  for   the 
fundamental   connexion   between   the   quantity   of    material 
changed  and  the  time  required  in  a  chemical  reaction. 

Wilhelmy  examined  the  inversion  of  cane  sugar  in  aqueous 
solution  in  the  presence  of  acids;  ClzH^On+  H2O  =  2C6H12O6. 
The  amount  of  change  at  any  moment  can  be  determined  by 
measuring  the  specific  rotatory  power  of  the  liquid. 

1  Lehrevon  der  Verwandshaft  [Dresden,  1777],  28. 

a  Essai,  1.  409.  3  Pogg.  Ann.  81.  413,  499. 


CH.  II.  §§173-175]  SIMPLEST  CASES.  357 

The  assumption  made  by  Wilhelmy  was  that  the  mass  of 
sugar  changed  in  unit-time  is  proportional  to  the  mass  of 
sugar  remaining  unchanged  in  the  reacting  system. 

Let  A  =  mass  of  sugar  originally  present;  let  x=  mass  ot 
sugar  changed  in  time  6  ;  then  the  ratio  of  the  amount 
changed,  dx,  to  the  time,  dO,  is  given  by  the  equation 


where  A—xh  the  amount  of  unchanged   sugar   and   c  is 
a  constant. 

The  ratio  -—  expresses  the  velocity  of  the  chemical  change, 

or,  in  shorter  words,  the  reaction-velocity. 

Ostwald1  integrates  the  above  equation  to  get  it  into  a 
form  in  which  it  may  be  applied  ;  he  counts  the  time  from 
the  moment  when  the  sugar  solution  is  brought  into  contact 
with  the  acid,  i.e.  when  0  =  o  and  x  =  o.  The  final  form  in 
which  the  value  of  the  constant  appears  is 


i  A 

The  numbers  shew  that  ^  log  -=  -  is  nearly  constant  for 
u        A  —x 

values  of  0  varying  from  15  to  630  minutes. 

Later  experiments  conducted  by  Ostwald2  on  the  in- 
version of  cane  sugar  have  confirmed  the  result  of  Wilhelmy, 
that  the  reaction-velocity  at  each  moment  is  proportional  to 
the  mass  of  sugar  capable  of  undergoing  change. 
75  Experiments  conducted  by  different  chemists  with  dif- 
ferent changing  systems  have  shewn  that  the  result  obtained 
by  Wilhelmy  holds  good  in  very  many  and  very  different 
cases.  This  result  may  be  stated  in  these  words  :  — 

TJie  amount  of  chemical  change  at  any  moment  is  pro- 
portional to  the  mass  of  the  changing  body  in  the  system. 

Among  the  more  important  researches  which  have  es- 
tablished the  accuracy  of  this  statement  may  be  mentioned, 
Harcourt  and  Esson's  examination  of  the  reaction  between 

1  Lehrbuch,  2.  617?  2  J.fiirprakt.  Chemie  (2).  29.  385. 


358  VELOCITY  OF  CHEMICAL  CHANGE.         [BOOK  II. 

potassium  permanganate  and  a  large  excess  of  oxalic  acid l, 
and  the  reaction  between  peroxide  of  hydrogen  and  hydriodic 
acid2;  Ostwald's  examination  of  the  catalytic  change  of 
methylic  acetate  to  methylic  alcohol  and  acetic  acid  in 
presence  of  different  acids8;  van't  Hoff's  examination  of  the 
change  of  dibromosuccinic  acid  (from  fumaric  acid)  to  bromo- 
malei'c  acid  and  hydrobromic  acid  by  boiling  with  water,  and 
of  monochloracetic  acid  to  glycollic  acid  and  hydrochloric 
acid  in  presence  of  water4. 

T  A 

In  all  these  cases  the  value  of  the  expression  ^  log  is 

v          jci  —  X 

nearly  constant8.  The  fact,  that  the  velocity  of  the  early  stages 
of  a  chemical  change  is  often  different  from  the  velocity  when 
the  change  has  proceeded  for  a  little  time,  introduces  a  possible 
source  of  error  into  the  observations  on  which  the  statement 
concerning  the  proportionality  between  the  rate  of  change  and 
the  mass  of  the  changing  body  is  based.  But  this  error  may 
be  obviated  by  counting  the  time  from  the  moment  when  the 
velocity  of  the  change  becomes  regular,  or  by  determining 
the  reaction-velocity  for  definite  intervals  while  the  change 
proceeds 6. 

The  outcome  of  these  experiments  then  is  to  establish 
a  simple  relation  between  the  quantity  of  a  body  undergoing 
chemical  change  and  the  time  occupied  in  accomplishing  the 
change.  In  all  cases  only  one  body  was  undergoing  change, 
or  if  more  than  one  actually  underwent  change  then  the 
masses  of  all  except  one  were  made  so  large  that  changes 
in  these  masses  could  practically  be  neglected.  It  is  also 
to  be  noted  that  all  the  changing  systems  examined  were 
homogeneous;  no  separation  of  gases  or  solids  occurred 
during  the  various  processes.  With  these  limitations,  it 
appears  that  chemical  change  obeys  the  same  law  as  gravi- 

1  Phil.  Trans,  for  1866.  193.  2  Phil.  Trans,  for  1867.  117. 

3  J-furprakt.  Chemie  (2).  28.  449. 

4  Etudes  de  dynamique  chitnique  [Amsterdam,  1884],  14. 

5  For  details  of  the  methods  used  for  measuring  the  velocities  of  these  changes, 
and  for  tables  shewing  the  actual  and   observed   values  of  the  constant,    see 
Ostwald's  Lehrbuch,  2.  616—624. 

6  See  Ostwald,  loc.  cit.  624. 


CH.  II.  §§175,  176]     MORE   COMPLEX   CASES.  359 

tative,    electrostatic,    electrodynamic,    electromagnetic,    and 
other  physical  changes. 
.76        But  we  must  now  proceed  to  cases  where  more  than  one 
body  undergoes  chemical  change  at  the  same  time. 

If  we  assume  that  the  amount  of  'change  which  each 
member  of  the  system  undergoes  is  proportional  to  the  active 
mass  of  that  body,  then  the  product  of  the  active  masses  of 
all  the  changing  bodies  gives  the  function  which  expresses 
the  velocity  of  the  complete  reaction. 

In  order  to  find  whether  this  assumption  is  justified  by 
facts,  Ostwald1  begins  by  finding  an  expression  for  the 
reaction-velocity  when  two  bodies  only  are  concerned.  Let 
A  and  B  represent  the  masses  of  the  bodies  originally 
present,  and  let  x  =  the  portion  of  each  changed  in  the  time 
0,  these  masses  being  measured  in  equivalents;  then  the 
reaction-velocity  is 

~Q=(A-x}(B-x}c, 

where  c  is  a  constant. 

If  equal  numbers  of  equivalents  of  the  two  bodies  are 
concerned  in  the  change  then  A  =  B,  and 

dx    .  . 

-^(A-^c. 

By  integration,  taking  x  and  6  simultaneously  equal  to 
zero,  the  equation 


-— 
A  —x 

is  obtained. 

If  the  fundamental  assumption  is  correct,  the  product  Ac 

must  remain  constant  when  x  varies  :  Ac=  -*.  —.  -  . 

(J    /i  —X 

The  experiments  made  by  Hood2  on  the  change  of 
potassium  chlorate  and  ferrous  sulphate  in  acid  solution  to 
potassium  chloride  and  ferric  sulphate,  are  used  to  test  the 
accuracy  of  the  equation.  In  these  experiments  9  varied 
from  20  to  520  minutes,  and  Ac  was  almost  constant,  ranging 
from  '00737  to  -00760;  when  6  became  628  and  639  mins. 

1  Lehrbuch,  2.  626—634.  !  PkU.  Mag,  (5).  6.  371. 


360  VELOCITY  OF  CHEMICAL  CHANGE.         [BOOK  II. 

Ac  became  -00726  and  -00725,  but  in  these  cases  A  —  x  was  so 
small  that  the  calculation  of  Ac  is  uncertain. 

Among   other  determinations  whereby  values  are  found 

for  the  function  ^.-j  --  are  (i)  Warder's  measurements  of 
tj  A.  —x 

the  rate  of  saponification  of  ethylic  acetate  by  caustic 
soda1;  (2)  Ostwald's  determination  of  the  rate  of  change  of 
acetamide  in  presence  of  an  acid  into  acetic  acid  and  the 
ammonium  salt  of  the  acid  used2;  and  (3)  van't  Hoff's 
experiments  on  the  velocity  of  the  reaction  wherein  sodium 
monochloracetate  and  soda  are  changed  to  sodium  glycollate 
and  sodium  chloride3.  In  the  first  set  of  experiments  the 
rate  of  change  was  determined  by  titrating  from  time  to  time 
with  a  standard  acid  ;  in  Ostwald's  experiments  the  rate  of 
change  was  determined  by  decomposing  the  unchanged 
acetamide  by  sodium  hypochlorite  and  measuring  the  nitrogen 
evolved  ;  and  in  the  third  case  van't  Hoff  measured  the 
amount  of  change  in  specified  times  by  titrating  the  residual 
soda  by  means  of  a  standard  acid. 

In  each  set  of  experiments  Ac  has  a  nearly  constant 
value;  the  value  varies  from  "106  to  "113  in  Warder's  ex- 
periments where  6  varies  from  5  to  120  minutes  ;  in  Ostwald's 
experiments  Ac  varies  from  -0087  to  -0092,  6  varying  from 
15  to  240  minutes;  and  in  van't  Hoff's  experiments,  where  6 
varies  from  9  to  374  minutes,  Ac  varies  from  '00551  to  -00633. 

The  expression  already  given  for  the  reaction-velocity 
when  the  two  bodies  undergoing  change  are  present  in  equal 
numbers  of  equivalents  is  applicable  with  some  modification 
when  an  excess  of  one  of  the  reacting  bodies  is  employed4. 
In  this  case  A  is  not  equal  to  B  and  on  integrating  the 

equation  —-  =  (A  —  x}  (B  —  x)  c,  we  obtain  the  expression 


Hood5   determined   the   rate   of    the    change    occurring 

1  Amer.  C.  Journal  for  1882.  No.  5.         2  J.  fur  prakt.  Chemie  (2).  27.  i. 
3  Etudes  de  dynamique  chimique,  20.         4  See  Ostwald,  loc.  cit.  631. 
6  Phil.  Mag.  (5).  6.  378. 


CH.  II.  §§  176,177]    CO-EXISTENCE  OF  REACTIONS.  361 

between  ferrous  sulphate  and  potassium  chlorate  when  an 
excess  of  one  of  the  salts  was  used:  In  one  case  there  was 
twice  as  much  chlorate  employed  as  was  required  for  the 
reaction ;  and  in  the  other  case  four  times  as  much  ferrous 
sulphate  as  was  required.  If  A  —  FeSO4  and  £=KC\O3, 
then  in  the  first  case  A  =  2B,  and 

A-X- 


and  in  the  second  case  B  =  ^A,  and 
A-*- 


The  actual  value  found  for  Ac  in  the  first  set  of  experi- 
ments varied  from  '001965  to  '00202,  0  varying  from  30*5 
to  360  minutes  ;  and  the  actual  value  found  for  Ac  in  the 
second  case  varied  from  -00411  to  '00431,  0  varying  from 
24  to  231  minutes. 

There  is  then  ample  experimental  evidence  in  support  of 
the  assertion  that  when  more  than  one  body  is  simultaneously 
undergoing  chemical  change  the  rate  of  the  change  is  pro- 
portional to  the  product  of  the  active  masses  of  all  the  bodies 
in  the  changing  system  1. 

177  The  foregoing  treatment  of  the  relation  between  the  rate 
of  a  chemical  change  and  the  amount  of  the  changing  bodies 
implies,  that  if  more  than  one  substance  is  undergoing  change, 
each  obeys  the  law  of  mass-action,  and  each  change  proceeds 
as  if  it  were  independent  of  the  others.  The  truth  of  this 
proposition  is  rendered  apparent  by  the  close  agreement 
between  the  observed  rates  of  many  different  chemical 
reactions  and  the  values  calculated  on  the  assumption  that 
the  amount  of  change  at  any  moment  of  any  one  member  of 
the  system  is  proportional  to  the  active  mass  of  this  body, 
and  the  total  change  at  any  moment  is  proportional  to  the 
product  of  the  active  masses  of  all  the  changing  bodies. 

1  Ostwald,  loc.  cit.  632 — 634,  develops  the  necessary  equations  for  more 
complex  reactions  than  those  we  have  considered,  but  these  equations  cannot  yet 
be  applied  for  lack  of  experimental  data. 


362  VELOCITY  OF   CHEMICAL  CHANGE.          [BOOK  II. 

This  proposition  is  called  by  Ostwald  the  principle  of  the 
co-existence  of  reactions. 

Many  of  the  reactions  considered  in  the  previous  para- 
graphs have  been  regarded  as  more  simple  than  they  really 
are ;  small  secondary  changes  have  been  overlooked.  For 
instance,  when  methylic  acetate  reacts  with  water  in  the 
presence  of  an  acid  to  produce  acetic  acid  and  methylic 
alcohol,  the  rate  of  change  is  influenced  by  the  acetic  acid 
produced.  If  these  secondary  changes  are  taken  into  account 
in  the  calculation  of  the  theoretical  constant  of  each  reaction, 
the  total  change  being  treated  as  made  up  of  the  primary 
change  and  one  or  more  small  secondary  changes,  the  values 
obtained  for  the  constant  shew  smaller  variations  than  if  the 
small  secondary  changes  are  overlooked.  But  this  is  exactly 
what  ought  to  be  if  the  principle  of  the  co-existence  of  re- 
actions is  true1. 

178  When  a  solid  and  a  liquid  interact  we  have  a  heterogeneous 
system.  The  amount  of  change  in  a  given  time  is  here  also 
proportional  to  the  product  of  the  active  masses  of  the  changing 
bodies.  But  the  active  mass  of  the  solid  is  proportional  to 
the  surface  exposed,  and  not  to  the  total  mass  of  the  solid. 
The  equation  by  which  the  reaction-velocity  can  be  calculated 
must  therefore  be  modified.  If  w  =  the  surface  of  the  solid 
the  equation  becomes 

-  =  (A-x\cw 
and  by  integration 

log  „        =cwd. 
&  A  —x 

It  is  difficult  to  apply  this  equation ;  the  results  of  ex- 
periments shew  a  certain  amount  of  variation  in  the  value  of 
what  ought  to  be  a  constant.  But  it  is  almost  impossible 
to  get  a  constant  surface  of  a  solid ;  the  solution  of  the  solid 
in  the  liquid  causes  the  action  to  slacken ;  gases  are  some- 
times formed  on  the  surface  and  the  surface  is  diminished, 
and  so  on2. 

1  Ostwald,  loc.  cit.  2.  636,  puts  the  principle  of  the  co-existence  of  reactions 
into  a  mathematical  form.  2  See  Ostwald,  loc.  cit.  2.  638—640. 


CH.  II.  §§  178-180]  METHODS  FOR  MEASURING  CHANGE.       363 


SECTION  II.     Chemical  Equilibrium. 

179  We  must  now  glance  at  the  statical  methods  whereby  it 
has  been    attempted  to  measure  chemical  forces.     In  these 
methods  a  chemical  system  is  brought  into  equilibrium  by 
opposing  a  change   in    one    direction    by   a   change   in   the 
opposite    direction,    and    the    distribution     of    the    various 
members    of    the    system    is    determined    when    equilibrium 
results. 

The  methods  which  are  applicable  here  are  either  chemical 
or  physical.  Chemical  methods  may  be  used  in  cases  where 
the  system  is  heterogeneous  and  one  or  more  of  the  members 
of  the  system  can  be  measured  by  some  ordinary  analytical 
process  without  disturbing  the  equilibrium  which  the  system 
has  attained ;  for  instance,  an  acid  reacts  with  an  insoluble 
salt  of  another  acid  forming  a  soluble  salt  and  a  new  acid — 
e.g.  calcium  oxalate  and  hydrochloric  acid  produce  calcium 
chloride  and  oxalic  acid — the  soluble  acid  or  salt  may  be 
determined  in  a  portion  of  the  system  when  equilibrium  has 
been  reached.  Physical  methods  may  be  used  in  cases  where 
the  system  is  homogeneous  and  where  the  removal  of  any 
portion  of  a  member  of  the  system  would  disturb  the  equi- 
librium of  the  system  :  in  these  methods  either  a  physical 
change  which  accompanies  and  forms  the  measure  of  the 
chemical  change  is  measured ;  or  a  physical  property  is 
measured  the  value  of  which  is  dependent  on  the  distribution 
of  the  chemically  reacting  bodies  \ 

180  If  a  body  A  is  changed  to  A',  and  if  A'  is  changed  to  A, 
the  system  will  attain  equilibrium  when  the  velocity  of  the 
primary  change  is  equal  to  that  of  the  reverse.     Let  /  be  the 
active  mass  of  A,  and/'  the  active  mass  of- A'',  let  x  be  the 
number  of  equivalents  of  A  changed  to  A',  and  let  x  be  the 
number  of  equivalents  of  A'  changed  to  A,  at  any  moment; 

1  Steinheil  (Annalen,  48.  153  [1843])  was  tne  fifst  to  &ive  a  general  statement 
of  the  theory  shewing  the  dependence  of  physical  properties  of  a  chemical  system 
on  changes  in  the  arrangement  of  the  members  of  the  system.  The  theory  is 
given  in  detail  in  Ostwald's  Lehrbuch,  2.  753 — 759. 


364  CHEMICAL  EQUILIBRIUM.  [BOOK  II. 

then  the  velocity  of  the  direct  change  f  J  is 


and  the  velocity  of  the  reverse  change  \—jn  \  1S 

®-</---v: 

But  x  must  equal  —x  and  dx=  —  dx'\  so  that 


And  therefore  the  reaction-velocity  of  the  whole  change, 

dx   . 

JQ,  is  expressed  as 


The  condition  of  equilibrium  is    ,.  =  o  ;  therefore,  if  £  is 
the  value  obtained  by  x  when  equilibrium  results 


Now  as  p  —  %  is  the  mass  (in  equivalents)  of  the  body  A, 
and  /'  +  £  is  the  mass  of  A',  present  in  the  system  when 
equilibrium  results,  and  as  these  masses  are  independent  of 
the  original  values  of  p  and  /',  the  equation  shews  equi- 
librium to  result  in  a  system  of  two  chemically  interacting 
bodies  when  the  active  masses  of  the  bodies  are  in  the 
same  ratio  as  the  velocity-constants  of  the  primary  and 
reverse  changes. 

The  value  of  £  can  be  determined  experimentally,  and 
from  this  the  ratio  of  the  velocity-constants  of  the  two  parts 
of  the  change  can  be  calculated. 

If  one  of  the  two  bodies  is  in  a  different  state  of  aggregation 
from  the  other,  then  the  active  mass  of  one  is  constant  ;  thus 
if  the  system  is  composed  of  a  solid  and  a  liquid  or  a  gas, 
the  active  mass  of  the  solid  is  constant  towards  the  liquid  or 
gas;  hence,  in  such  a  case  the  active  mass  of  the  other 


CH.II.§l8o]  SYSTEMS   OF   TWO   BODIES.  365 

constituent  must  also  be  constant  in  order  that  equilibrium 
may  result.  Such  cases  are  comparatively  simple ;  and  they 
comprise  by  far  the  greater  number  of  cases  in  which  the 
equation  of  equilibrium  for  a  system  composed  of  two 
changing  bodies  can  at  present  be  applied. 

The  case  of  water  in  contact  with  ice  at  o°  is  a  typical 
one.  Equilibrium  is  independent  of  the  mass  of  the  ice  ;  and 
as  the  mass  of  water  in  unit  volume  of  the  system  is  inde- 
pendent of  the  absolute  mass,  it  follows  that  a  mixture  of 
ice  and  water,  in  any  proportion,  remains  in  equilibrium  at  o°. 
But  if  the  system  is  compressed  the  active  mass  of  the  water 
is  increased,  and  therefore  equilibrium  is  upset,  and  is  restored 
again  only  at  a  temperature  lower  than  o°.  If  a  solid  ex- 
pands on  melting,  then  equilibrium  between  this  solid  and 
its  own  liquid  is  attained  under  pressure  only  at  tempera- 
tures higher  than  that  of  the  normal  melting  point  of  the 
solid. 

So  also  in  cases  of  evaporation  of  liquids,  equilibrium 
results  at  a  definite  temperature  when  the  active  mass  of  the 
vapour  bears  a  certain  constant  ratio  to  that  of  the  liquid  ; 
to  maintain  the  constancy  of  this  ratio  the  active  mass  of  the 
vapour  must  remain  constant,  but  this  is  done  by  keeping  the 
pressure  constant.  The  constancy  of  the  pressure  of  a  vapour 
over  a  liquid  is  therefore  a  function  of  the  temperature,  and 
not  of  the  relative  quantities  of  vapour  and  liquid. 

Cases  of  solution  belong  to  the  category  we  are  now 
discussing.  When  a  salt  dissolves  in  water  the  active  mass 
of  the  solid  is  constant,  and  therefore  equilibrium  must  result 
when  a  definite  mass  of  the  solid  has  dissolved,  and  must  be 
independent  of  the  relative  masses  of  dissolved  and  undis- 
solved  salt  but  dependent  on  the  temperature. 

The  attainment  of  equilibrium  in  many  cases  of  allotropic 
change  is  also  conditioned  by  the  constancy  of  the  ratio 
of  the  active  masses  of  the  changing  bodies.  For  instance, 
in  the  change  of  paracyanogen  (CN)n  to  gaseous  cyanogen 
(CN)2  equilibrium  results  when  the  gas  attains  a  certain 
pressure  which  is  independent  of  the  mass  of  paracyanogen 
present  but  varies  as  the  temperature  varies. 


366  CHEMICAL.  EQUILIBRIUM.  [BOOK  II. 

So  also  with  red  and  yellow  phosphorus1.  If  red 
phosphorus  is  heated  to  440°  the  pressure  of  the  vapour 
increases  up  to  a  limit  which  is  independent  of  the  mass  of 
solid  phosphorus  present ;  but  on  continued  heating  the 
pressure  falls  until  it  again  attains  a  constant  value.  If  yellow 
phosphorus  is  heated  to  440°  the  pressure  of  the  vapour  is 
much  greater  than  that  from  red  phosphorus  at  the  same 
temperature;  but  the  pressure  falls  until  it  attains  the  same 
value  as  that  which  marks  the  final  equilibrium  between  red 
phosphorus  and  its  vapour  at  the  same  temperature.  The 
results  are  represented  graphically  in  the  accompanying 
curve. 

Troost  and  Hautefeuille  have  shewn  that  red  phosphorus 
exhibits  different  properties  according  to  the  temperature  at 


Yellow 


Red 


which  it  is  prepared.  Red  phosphorus  at  440°  gives  a  certain 
vapour-pressure  ;  equilibrium  results  when  the  active  mass  of 
the  gas  has  attained  a  certain  value,  and  this  value  depends 
on  the  pressure ;  but  on  continued  heating  another  variety  of 
red  phosphorus  is  produced,  and  therefore  the  active  mass 
changes,  and  therefore  the  pressure  changes  until  equilibrium 
again  results.  Yellow  phosphorus  at  440°  gives  a  certain 
vapour-pressure;  but  the  composition  of  the  vapour  is 
changing,  and  therefore  the  pressure  changes  until  the 
vapour  attains  a  definite  composition,  when  its  active  mass 
becomes  constant  and  equilibrium  results 2. 

1  Hittorf,  Pogg.  Ann.  126.  193 ;  Troost  and  Hautefeuille,  Ann.  Chim.  Phys. 
(5).  2.  153;  Lemoine,  Ann.  Chim.  Phys.  (4).  24.  129. 

2  For  a  more  detailed  discussion  of  these  and  other  cases  of  equilibrium  in 
heterogeneous  systems  composed  of  two  constituents,  see  Ostwald's  Lehrbtich,  2. 
643—650. 


CH.  II.  §§  1  80,  l8l]    SYSTEMS  OF  FOUR  BODIES.  367 

181        Let  us  now  briefly  consider  the  equilibrium  of  a  system 
comprising  four  changing  bodies. 

Let  the  two  bodies  A  and  B  be  changed  to  A'  and  B'\ 
let  the  active  masses  (in  equivalents)  of  the  four  bodies 
originally  present  be  /,  g,  p',  and  q  ',  respectively;  and  let 
x  be  the  number  of  equivalents  of  A  and  B  changed  to 
A'  and  B',  and  x'  the  number  of  equivalents  of  A'  and  B 
changed  to  A  and  B,  at  any  moment  ;  then  the  velocity  of 
the  direct  change  is  expressed  by  the  equation 


and  the  velocity  of  the  reverse  change  by  the  equation 


and  therefore  the  velocity  of  the  complete  change  is 


and  the  condition  of  equilibrium,  i.e.  the  condition  under 
which  -JQ  =o  and  x=%  (s.  par.  180)  is  given  by  the 
equation1 


The  simplest  case  in  which  to  apply  this  equation  is 
obtained  by  using  equivalent  quantities  of  A  and  B  and 
allowing  these  to  react  without  the  addition  of  either  A' 
or  B'  ;  in  this  case  p  =  q=  i  and  /'  =  q  =  o,  and  therefore 
(i  _£)V=f  </,hence 


The  value  of  £  i.e.  amount  of  A  and  B  changed,  and  that 
of  i  —  £  i.e.  amount  of  A  and  B  remaining  unchanged,  is 
determined  experimentally,  and  from  these  values  the  ratio 
of  the  velocity-constants  is  calculated. 

1  This  equation  is  identical  with  that  obtained  by  Guldberg  and  Waage  for  the 
equilibrium  of  a  system  of  four  bodies,  but  the  constants  c  and  c'  appear  here  as 
reaction-velocities,  not  as  '  forces.' 


368  CHEMICAL  EQUILIBRIUM.  [BOOK  II. 

/     fc    \2 
Ostwald  calls  the  ratio  [—3^]    the  partition -coefficient  of 

the  reaction ;  the  ratio  of  the  velocity-constants  in  this  case  is 
equal  to  the  square  root  of  the  partition-coefficient 
182        Three  important  series  of  experiments  with  homogeneous 
systems  have  given  results  to  which  the  equation 


can  be  applied:  these  are  Thomsen's  measurements  of  the 
quantities  of  heat  produced  by  the  interaction  between  an 
acid  and  the  neutral  salt  of  another  acid  ;  Ostwald's  measure- 
ments of  the  specific  volumes  of  the  solutions  obtained  by 
mixing  an  acid  with  the  neutral  salt  of  another  acid  ;  and 
Berthelot  and  P.  de  Saint  Gilles'  determinations  of  the  amount 
of  ethereal  salt  formed  when  equilibrium  results  between  an 
acid  and  an  alcohol. 

183  Thomsen's  experiments  are  based  on  the  proposition  that 
if  the  heat  of  neutralisation  of  an  acid  by  a  base  is  x  units, 
and  the  heat  of  neutralisation  of  another  acid  by  the  same 
base  is  y  units,  the  heat  produced  on  mixing  equivalent 
masses  of  the  two  acids  with  the  base  will  be  z  units,  and 
z  will  be  equal  to  x,  or  equal  to  yt  or  will  be  a  number 
between  x  and  y,  and  that  from  observations  of  x,  y,  and  z 
just  conclusions  can  be  drawn  as  to  the  partition  of  the  base 
between  the  acids. 

The  acids  chosen  to  begin  with  were  nitric  and  sulphuric, 
and  the  base  was  soda.  Whether  nitric  acid  is  added  to 
an  equivalent  quantity  of  sodium  sulphate,  or  sulphuric  acid 
to  an  equivalent  quantity  of  sodium  nitrate,  or  equivalent 
quantities  of  soda,  nitric  acid,  and  sulphuric  acid  are  mixed, 
the  distribution  of  the  reacting  bodies  when  equilibrium 
results  will  be  the  same,  and  the  thermal  value  of  the 
change  will  be  the  same 1. 

Sulphuric  acid  and  soda  were  mixed  in  equivalent 
quantities  in  dilute  aqueous  solution  (SO3  +  2OoH2O  and 

1  This  proposition  may  be  deduced  from  the  principles  of  thermal  chemistry ; 
it  has  also  been  experimentally  proved  by  Thomsen;  see  Pogg.  Ann.  138.  65  ;  or 
Thermochemische  Untersnchungen,  1.  98. 


CH.  II.  §§  182,183]          THERMAL   METHODS.  369 

Na2O  +  2OOH2O),  the  quantity  of  heat  produced  was  31,380 
gram-units.  The  quantity  of  heat  which  disappeared  when 
sulphuric  acid  was  added  to  sodium  sulphate  in  dilute  aqueous 
solution  was  determined  for  different  proportions  of  the  acid 
and  salt ;  the  result  can  be  expressed  by  the  equation 

[>H2SO4Aq,  Na2SO4Aq]  =  -  -^  3300  gram-units. 

If  therefore  I  +  n  equivalents  of  sulphuric  acid  react  with 
an  equivalent  of  soda  the  thermal  value  of  the  change  may  be 
expressed  thus 

[i  +  ;*H2S04Aq,  NafOAq]  =  31,380-^3,300. 

Nitric  acid  and  soda  were  then  mixed  in  dilute  solution 
(N2Oe  +  2OoH2O  and  Na2O +  2OoH2O);  the  quantity  of  heat 
produced  was  27,230  gram-units.  The  quantity  of  heat 
which  disappeared  when  nitric  acid  was  added  to  sodium 
nitrate  in  dilute  solution  was  80  gram-units ;  this  is  so  small 
that  it  may  be  neglected,  and  the  reaction  between  equiva- 
lent quantities  of  nitric  acid  and  soda  may  be  expressed 
thermally  as 

[H'N206Aq,  Na'OAq]  =  27,230. 

Equivalent  quantities  of  nitric  acid  and  sodium  sulphate 
in  dilute  solution  were  then  mixed  ;  the  quantity  of  heat 
which  disappeared  was  3,500  units.  Now  if  the  sole  products 
of  the  reaction  between  equivalent  quantities  of  nitric  acid 
and  sodium  sulphate  in  dilute  solution  were  sulphuric  acid 
and  sodium  nitrate,  the  quantity  of  heat  which  would  dis- 
appear in  this  reaction  would  be  equal  to  the  difference 
between  the  heat  of  neutralisation  of  nitric  acid  and  that 
of  sulphuric  acid  by  soda l ;  this  quantity  is 

27,230-31,380-  -4,150. 

But  the  quantity  of  heat  which  was  actually  used  was 
3,500 ;  therefore  the  whole  of  the  sodium  sulphate  had  not' 
been  changed  to  sodium  nitrate,  and  therefore  the  system 
when  in  equilibrium  contained  sodium  nitrate  and  sulphate 
and  also  nitric  acid  and  sulphuric  acid.  And  moreover,  if  the 

1  [Na2S04Aq,  N2O5Aq]  =  [Na2OAq,  N2O5Aq]-[Na2OAq,  SO3Aq]. 
M.  C.  24 


3/0  CHEMICAL  EQUILIBRIUM.  [BOOK  II. 

only  reaction  which  occurred  between  sodium  sulphate  and 
nitric  acid  were  formation  of  sodium   nitrate  and  sulphuric 

acid,  we  might  conclude  that  — —  (=  '84)  parts  of  the  sulphate 

had  been  changed. 

But  we  know  that  the  sulphuric  acid  produced  in  the 
change  would  react  with  the  unchanged  sodium  sulphate 
with  disappearance  of  heat ;  this  must  be  taken  into  account 
in  the  calculation. 

Let  |  be  the  number  of  equivalents  of  sodium  sulphate  which 
have  been  decomposed  by  the  nitric  acid,  then  £  will  also  be  the 
number  of  equivalents  of  sodium  nitrate  formed,  and  also  the 
number  of  equivalents  of  sulphuric  acid  formed,  and  I—  £  will 
be  the  number  of  equivalents  of  sodium  sulphate  remaining;  the 
total  thermal  change  will  therefore  consist  of  three  parts;  — 

(1)  decomposition  of  £  Na2SO4  =  -£3i,38o, 

(2)  formation  of  £  Na2N2O6        =  +  f 27,230, 

(3)  reaction  between  £  H2SO4  and  i  -£Na2SO4. 

The  thermal  value  of  (3)  will  be  found  by  using  the  equation 
already  given  ;  this  equation  will  now  assume  the  form 


3>300. 


As  the  observed  thermal  value  of  the  complete  reaction 
was  —  3,500  we  have  the  equation 
[Na2SO4Aq,  H2N2O6Aq] 


=  -3,500  =  £(27230-  31380)-  (i  -£)---  3,300. 

rV8 

Thomsen  found  that  if  £  is  taken  as  f,  the  calculated  value 
of  the  equation  is  —3550,  which  is  almost  identical  with  the 
observed  value. 

Applying  the  equation  of  equilibrium  given  in  par.  182 
to  the  reaction  between  sodium  sulphate  and  nitric  acid,  the 


CH.  II.  §183]  THERMAL  METHODS.  371 

value  of  £  is  found  to  be  f ;  hence,  as 

c      (    % 


it  follows  that  -,  —  4  ;  i.e.  the  ratio  of  the  velocity-constants  of 
the  direct  and  reverse  changes  is  4. 

By  substituting  these  values  for  -,  and  £  in  the  equation  of 
equilibrium  given  in  par.  181,  viz. 


equations  are  obtained  which  can  be  applied  to  find  the 
thermal  values  of  the  change  occurring  between  different 
quantities  of  nitric  acid  and  sodium  sulphate  in  presence 
of  varying  masses  of  sulphuric  acid  or  sodium  nitrate.  Thus, 
to  take  one  case,  let  p,  q,  p',  and  q'  represent  the  masses 
(in  equivalents)  of  nitric  acid,  sodium  sulphate,  sulphuric 
acid,  and  sodium  nitrate,  respectively;  let  q—i^p'  =  q'  =  o, 
and  let  p  be  variable  ;  we  have 


Thomsen  measured  the  thermal  change  when  /  varied  ; 
the  following  table  presents  the  observed  and  calculated 
values : — 

Gram-units  of  heat  disappeared. 

p     .  £  Calculated.  Observed. 

\  '121  920  900 

\  -232  l66o  1620 

\  -423  2660  2580 

1  "667  3550  3500 

2  '849  3950  4050 

3  -903        4040        4100 

The  differences  are  within  the  limits  of  the  experimental 
errors. 

Other  series  of  experiments  were  conducted,  (i)  in  which 
/  =  2,  g=i,  q'  =  o,  and  ff  varied  from  o  to  3 ;  (2)  in  which 
q  =  q  —  I,  /'  =  o,  and  /  varied  from  \  to  I  ;  and  (3)  in  which 
p  =  q  =  o,  q  =  i ,  and  p'  varied  from  I  to  2 ;  in  all  these  ex- 

24—2 


372  CHEMICAL   EQUILIBRIUM.  [BOOK  II. 

periments  the  observed  values  agreed  well  with  the  calculated 
values. 

Thomsen  also  conducted  experiments  with  sodium  sulphate 
and  hydrochloric  acid ;  here  also  it  was  found  that  f  of  the 
sodium  sulphate  was  decomposed,  and  therefore  in  this  reaction 

also  —  =  4.     The  proportions  of  the  reacting  bodies  were  then 

varied  and  numbers  were  obtained  which  agreed  well  with 
those  calculated  by  the  use  of  the  equation  of  equilibrium. 

Thomsen's  thermochemical  investigation  of  the  partition 
of  a  base  between  two  acids  fully  confirms  the  accuracy  of  the 
equation 


184  Ostwald's  experiments  are  based  on  measurements  of  the 
specific  gravities  of  solutions  of  equivalent  quantities  of  acids 
and  bases  and  of  the  salts  obtained  by  the  reactions  of  these 
acids  and  bases,  and  also  of  the  liquids  formed  when  two  of 
the  acids  are  mixed  with  an  equivalent  quantity  of  one  of 
the  bases.  The  following  example  illustrates  Ostwald's 
method  : — 

(i)     Sp.  gr.  of  solution  of  caustic  soda  (approx.  normal)  [i  vol.] 
(ii)     Sp.  gr.  of  an  equivalent  solution  of  sulphuric  acid  [i  vol.] 
(iii)    Sp.  gr.  of  solution  of  sodium  sulphate  [2  vols.] 

(i)     1-04051 1-04051 

(ii)     1*02970  Nitric  acid  [i  vol.]     1-03083 

Sum     2-07021  Sum    2-07134 

(iii)    2-05918         Sodium  nitrate  [2  vols.]     2-05266 

Diff. -0-01103  Diff. -0-01868 

The  increase  in  spec.  grav.  accompanying  the  neutralisation 
of  soda  by  nitric  acid  is  greater  by  '00765  than  the  increase 
which  accompanies  the  neutralisation  by  sulphuric  acid. 

Now  if  sodium  sulphate  and  nitric  acid  do  not  react  when 
mixed,  the  spec,  gravity  of  the  mixed  solution  would  be 
Sodium  sulphate  [2  vols.]    2*05918 
Nitric  acid  [i  vol.]     1*03083 

Sum     3*09001 
But  the  observed  spec.  grav.  was  [3  vols.]    3*08343 


Diff. -0-0065 8 


CH.II.§l84]  VOLUMETRIC   METHODS.  373 

If  the  nitric  acid  and  sodium  sulphate  had  been  completely 
changed  to  sodium  nitrate  and  sulphuric  acid,  the  change  in 
spec,  gravity  would  have  been  —  -0076$  ;  thus 

Sodium  nitrate  [2  vols.]    2-05266 
Sulphuric  acid  [r  vol.]     1*02970 

Sum    3*08236 
Sod.  sulphate  [2  vols.]  +  nitric  acid  [i  vol.]     3-09001 


Diff.  -  0*00765 

Therefore  when  sodium  sulphate  and  nitric  acid  react 
in  equivalent  quantities  the  greater  part,  but  not  the  whole, 
of  the  soda  goes  into  combination  with  the  nitric  acid. 

Before  the  exact  distribution  of  the  soda  between  the  two 
acids  can  be  determined,  it  is  necessary  to  measure  the  changes 
in  spec,  gravity  which  may  accompany  secondary  reactions. 
Ostwald's  measurements  shewed  that  the  observed  spec. 
gravity  agreed  with  the  calculated,  within  the  limits  of  ex- 
perimental error,  (i)  when  solutions  of  nitric  and  sulphuric 
acids  were  mixed,  (2)  when  sodium  nitrate  was  mixed  with 
sodium  sulphate,  (3)  when  sodium  nitrate  was  mixed  with 
nitric  acid.  But  when  sodium  sulphate  was  mixed  with 
sulphuric  acid  the  observed  spec,  gravity  was  greater  than 
that  calculated  on  the  assumption  that  no  chemical  change 
occurred;  the  increase  in  spec,  gravity  was  found  to  agree 
very  closely  with  that  calculated  by  the  interpolation-for- 


Ostwald  then  applied  this  correction,  and  arrived  at  the 
result  that  when  sodium  nitrate  and  sulphuric  acid  interact  in 
equivalent  quantities  in  dilute  aqueous  solution,  two-thirds 
of  the  soda  remains  combined  with  the  nitric  acid,  and  one- 
third  enters  into  combination  with  the  sulphuric  acid.  This 
result  is  identical  with  that  obtained  by  Thomsen.  A  similar 
examination  of  the  reaction  between  sodium  chloride  and 
sulphuric  acid  gave  a  result  the  same  as  that  which  Thomsen 
obtained. 

Hence  Ostwald's  volumetrical  investigation  of  the  partition 
of  a  base  between  two  acids  fully  confirm  the  accuracy  of  the 

equation  (/-£)(?-*)*  =  (/  +  £)  (tf  +  0  c'- 


374  CHEMICAL  EQUILIBRIUM.  [BOOK  II. 

185  Van't  Hoff1,  in  1877,  use^  tne  results  of  the  experiments 
of  Berthelot  and  P.  de  Saint  Gilles  on  the  etherification  of 
alcohols,  in  order  to  test  the  accuracy  of  the  equation  of 
equilibrium  which  he  had  deduced  independently  of  Guldberg 
and  Waage.  The  experiments  shewed  that  equilibrium  was 
established  in  a  mixture  of  equivalent  quantities  of  alcohol 
and  acetic  acid  when  two-thirds  of  the  alcohol  and  the  acid 
were  transformed  into  ethereal  salt  and  water  ;  therefore  here 

also  -7  =  4;  and  the  equation  for  calculating  £  when/  varies  is 


where/  =  active  mass  of  alcohol,  q  =  active  mass  of  acetic  acid, 
/'  =  active  mass  of  ethereal  salt,  q  =  active  mass  of  water  ; 
initial  conditions  being  q  =  I  and  />'  =  q  =  o. 

The  following  table  gives  some  of  the  results  :  — 

P  __  j  ___ 

Calculated.  Observed. 

•05  -049  -05 

•08  -078  -078 

•18  '171  '171 

•28  -232  '226 

'33  "3"  >293 

•50  -423  -414 

•67  -528  -519 

ro  -667  -673 

1-5  -785  -816 

2  -845  -87 
2-80  -895  -892 

3  -902  -90 
•945  -97 

In  another  set  of  experiments  p  =  q=\,p'  =  o>  and  q' 
was  variable;  the  calculated  values  of  £  agreed  well  with 
the  observed  values. 

By  these  experiments  the  equation  of  equilibrium  is  again 
verified. 
186        The  equation  of  equilibrium 


Ber.  10.  669. 


CH.  !!.§§!  85,  1  86]  VARIOUS  CASES.  375 

may  be  applied  to  heterogeneous  systems.  For  dealing  with 
systems  composed  of  solids  and  liquids  or  gases,  we  must 
distinguish  cases  in  which  one,  two,  or  three,  of  the  inter- 
acting bodies  are  solids  \ 

When  one  of  the  four   bodies   is   a   solid,  the  equation 
becomes 


where  h  =  active  mass  of  the  solid. 

If  the  initial  conditions  are  such  that/  =  ^=  I  and  /' 
we  have  the  equation 


by  means  of  which  the  ratio  of  the  reaction-velocities  can  be 
calculated  from  observations  of  h,  or  h  can  be  calculated  if 


-  is  known. 
c 


The  simplest  case  is  that  in  which  one  body  reacts  with 
the  solid,  the  other  two  bodies  being  absent  at  the  beginning 
of  the  reaction  ;  we  have/  =  ^  =  o,  and 

-  F 


This  last  case  is  considered  by  Ostwald  (he.  cit.}  in  detail, 
the  reacting  bodies  being  hydrochloric  acid  and  solid  calcium 

oxalate ;  the  values  obtained  for  -  h  are  not  constant.     This 

c 

reaction  therefore  shews  divergences  from  the  results  which 
ought  to  follow  if  the  law  of  mass-action  held  good.  But  it  is 
possible  to  reconcile  the  results  to  some  extent  with  deductions 
from  this  law ;  at  any  rate  the  experiments  of  Ostwald  do 
not  require  us  to  reject  the  law  of  mass-action,  but  they 
rather  open  a  path  which  will  probably  lead  to  fresh  dis- 
coveries concerning  chemical  equilibrium.  (See  Ostwald, 
he.  cit.} 

When  two  of  the  interacting  bodies  in  a  system  of  four 
bodies  are  solids,  the  other  two  being  liquids  or  gases,  the 
active  masses  of  the  solids  may  be  put  as  h  and  //,  re- 

1  Ostwald,  Lehrbuch,  2.  658—670. 


37°"  CHEMICAL   EQUILIBRIUM.  [BOOK  II. 

spectively,  and  the  equation  of  equilibrium  then  assumes  the 
following  form  ;  — 


and  therefore  —j-  =  -,  —  1  =  constant; 

or  in  words,  equilibrium  is  attained  when  the  active  masses  of 
the  two  liquid  or  gaseous  constituents  of  the  system  are  in  a 
fixed  ratio  which  is  independent  of  the  absolute  or  relative 
masses  of  the  two  solid  constituents. 

In  1871,  Deville  conducted  a  series  of  experiments  on  the 
reaction  between  iron,  iron  oxide,  water-gas,  and  hydrogen  \ 
In  these  experiments  water  was  heated  in  a  retort  connected 
with  a  tube  containing  iron,  the  other  end  of  the  tube  being 
in  connexion  with  a  mercury-pump  and  a  manometer.  A 
vacuum  having  been  obtained,  the  contents  of  the  retort,  as 
also  those  of  the  tube,  were  raised  to  a  constant  temperature, 
and  the  pressure  was  measured  by  the  manometer  ;  the 
pressure  was  composed  of  the  partial  pressures  of  the  water- 
gas  and  the  hydrogen  formed  by  the  reaction  between  the 
iron  and  the  steam.  As  the  reaction  consisted  of  a  direct 
change  of  steam  +  iron  to  hydrogen  +  iron  oxide,  and  a 
reverse  change  of  hydrogen  +  iron  oxide  to  steam  +  iron, 
equilibrium  ought  to  have  been  attained  when  the  active 
masses  of  the  steam  and  hydrogen  bore  a  constant  ratio 
to  each  other  at  a  specified  temperature.  As  the  active  mass 
of  a  gaseous  constituent  of  a  system  is  conditioned  by  the 
pressure,  it  follows  that  if  pv  =  the  partial  pressure  of  the 
hydrogen  and  pz  =  the  partial  pressure  of  the  water-gas,  the 

ratio  y  ought  to  have  been  constant  at  each  temperature. 

The  temperature  of  the  water  in  the  retort  was  kept  at  o°  in 
one  series  of  experiments,  and  at  10°  in  the  other  series  ;  the 
temperature  of  the  tube  varied  from  200°  to  1600°.  Small 
errors  might  readily  be  made  in  the  measurements  of  the 
pressures,  especially  at  the  higher  temperatures,  and  at  these 
temperatures  small  errors  would  considerably  affect  the 

1  Compt.  rend.  70.  1105;  71.  30. 


CH.  ii.  §  1 86]  VARIOUS  CASES.  377 

values  of  — .     The  following  table  shews  that  Deville's  results 
confirm  the  equation  of  equilibrium. 


/ 

A 

A 

a 

A 

A 

A 

A 
A 

200° 

•46 

9'59 

•048 

'97 

i9'53 

•os 

265 

•46 

6-42 

•072 

i'57 

23  '5  1 

•067 

360 

•46 

4-04 

•114 

•95 

7-63 

•124 

440 

•46 

2-58 

•178 

I  -01 

579 

•174 

860 

•46 

1-28 

•36 

1-30 

2-39 

•54 

1040 

•46 

•92 

•50 

1-27 

1-91 

•66 

1600 

•46 

'Si 

•90 

1-63 

1-17 

1-40 

The  experiments  of  Guldberg  and  Waage  on  the  reaction 
between  a  solution  of  potassium  carbonate  and  solid  barium 
sulphate  (referred  to  in  par.  170)  present  the  conditions  of 
equilibrium  of  a  system  composed  of  two  solid  and  two  liquid 
constituents.  Expressing  the  active  masses  of  the  soluble 
bodies,  potassium  carbonate  and  sulphate,  by  p  and  p',  the 

equation  of  equilibrium  asserts  that  the  ratio   —,  —  -..  should 

remain  constant  independently  of  the  masses  of  the  barium 
carbonate  and  sulphate.  The  following  numbers  exhibit  the 
values  actually  obtained  for  this  ratio  ;  — 


f        « 

200  o  39*5  4*06 

250  o  50-0  4-0 

350  o  71-9  3-87 

250  25  30-0  4-0 

300  25  40-8  3-94 

200  50  '5  3'95 

There  are  as  yet  but  few  data  by  which  may  be  tested 
the  correctness  of  the  deduction  from  the  equation  of  equi- 
librium, that  when  three  of  the  four  bodies  constituting  a  re- 
acting system  are  solids,  the  equilibrium  must  be  conditioned 
by  the  active  mass  of  the  liquid  or  gaseous  constituent  and 
must  be  independent  of  the  masses  of  the  three  solid  bodies. 

Isambert1  has  examined  the  equilibrium  of  the  system 
obtained  by  heating  together  solid  ammonium  chloride  and 

1  Cornet,  rend.  102.  1313. 


378  CHEMICAL  EQUILIBRIUM.  [BOOK  II. 

lead  oxide;  his  results  shew  that  when  equilibrium  is 
attained  for  a  specified  temperature,  the  pressure  of  the 
ammonia  gas  produced  in  the  reaction  is  constant  and  is 
independent  of  the  masses  of  the  solid  ammonium  chloride, 
lead  oxide,  and  lead  chloride  (or  oxychloride). 
187  We  have  now  passed  in  review  a  large  amount  of  varied 
experimental  evidence  which  establishes  on  a  firm  basis  the 
law  of  mass-action,  and  the  principle  of  the  co-existence  of 
reactions.  These  two  generalisations  assert  that  the  amount 
of  change  undergone  by  a  chemically  reacting  system  is  pro- 
portional to  the  product  of  the  active  masses  of  the  constituents 
of  the  system  and  the  coefficient  of  affinity  of  the  change,  and 
that  when  several  changes  take  place  simultaneously  the  total 
change  is  equal  to  the  sum  of  the  particular  changes.  We 
have  found  that  in  place  of  the  phrase  coefficient  of  affinity 
we  may  use  the  expression  reaction-velocity ;  but  we  have  not 
attempted  as  yet  to  analyse  the  conception  underlying  these 
expressions. 

The  law  of  mass-action  and  its  applications  to  different 
cases  of  chemical  change  have  been  treated  so  far  in  a  purely 
empirical  manner.  The  law  was  gained  by  determining  the 
distribution  of  the  reacting  bodies  in  certain  systems  which 
had  attained  equilibrium,  and  it  was  applied  to  determine  the 
conditions  of  equilibrium  in  other  systems  and  the  velocities 
of  the  reactions  which  occurred  before  equilibrium  was  at- 
tained. 

Besides  the  particular  methods  considered  in  the  preceding 
paragraphs  of  this  chapter,  there  are  two  general  methods  which 
may  be  used  in  attempts  to  solve  the  problems  of  chemical 
dynamics ;  one  of  these  is  thermodynamical,  and  the  other  is 
molecular. 


CH.  II.  §§  187,  1 88]  THERMODYNAMICAL  METHODS.  379 


SECTION  III.     Thermodynamical  methods  applied 
to  chemical  equilibrium*. 

188  Horstmann2,  in  1873,  propounded  a  thermodynamical 
theory  of  dissociation  which  is  also  generally  applicable 
to  other  cases  of  chemical  equilibrium,  inasmuch  as  the 
processes  which  occur  in  a  system  before  it  attains  chemical 
equilibrium  are  generally  reversible  processes.  Horstmann's 
method  consisted  in  applying  the  second  law  of  thermo- 
dynamics to  the  phenomena  of  dissociation;  he  concluded 
that  these  processes,  like  all  other  reversible  processes,  tend 
to  bring  the  system  to  that  condition  wherein  the  entropy  of 
the  system  has  attained  its  maximum  value  under  the  given 
conditions.  To  determine  the  conditions  under  which  the 
entropy  of  a  specified  system  undergoing  a  reversible  change 
becomes  a  maximum  is  therefore  to  determine  the  conditions 
of  equilibrium  of  that  system. 

Let   Q  =  quantity  of  heat  added  to  a  body  at  constant 

temperature   T,  then  ^.=  gain  of  entropy  to  the  body;   let 


Ql  =  quantity  of  heat  lost  by  a  body  at  constant  temperature 
Tv  then  -^  =  loss  of  entropy  to  the  body.  All  chemical 

and  physical  changes  occurring  spontaneously  are  accom- 
panied by  an  increase  in  the  entropy  of  the  system.  This 
statement  holds  good  for  non-reversible  changes;  but  as 
no  actually  occurring  change  is  completely  reversible  the 
statement  holds  for  all  changes. 

Suppose  that  one  of  two  bodies  is  hotter  than  another 
and  loses  heat  to  the  colder  ;  the  hotter  body  at  temperature 

7^  loses  heat  Q,  therefore  its  entropy  is  decreased  by  -^  ;  the 
colder  body  at  temperature  T9  gains  heat  Q,  therefore  its 

1  In  this  section  I  have  again  followed  Ostwald  ;  but  the  methods  discussed 
in  this  section  are  so  largely  physico-mathematical  that  I  have  attempted  only  the 
briefest  outline,  referring  the  student  to  Ostwald's  Lehrbuch,  2.  702  —  728,  and  to 
the  original  memoirs. 

'  Annalen,  170.  192. 


380  CHEMICAL  EQUILIBRIUM.  [BOOK  II. 

entropy  is  increased  by  -^  ;   but  as  7\  >  Ty  it  follows  that 
1 2 

•^  <  —  ;   in  other  words  the  entropy  of  the   system   is  in- 

*l  -*  2 

creased  by  the  passage  of  heat  from  the  hotter  to  the  colder 
body. 

Changes  of  state  involving  changes  of  pressure  and  volume 
are  also  accompanied  by  changes  of  entropy;  if  the  tempera- 
ture is  constant  the  entropy-change  is  easily  found  ;  if  volume 
and  temperature  change  simultaneously  with  pressure  the  total 
change  may  be  regarded  as  partly  adiabatic  until  the  final 
temperature  is  reached,  and  then  isothermal  until  the  system 
attains  equilibrium  ;  the  latter  part  of  the  change  is  alone 
accompanied  by  a  change  of  entropy.  As  it  is  possible  to 
pass  from  any  given  state  of  a  system  to  any  other  by  a 
path  which  is  partly  adiabatic  and  partly  isothermal,  it  is 
possible  to  lay  down  the  principles  on  which  the  entropy- 
change  accompanying  any  material  change  may  be  de- 
termined. 

189  The  application  of  thermodynamical  methods  to  the  study 
of  chemical  equilibrium  has  been  much  developed  by  Willard 
Gibbs1. 

Gibbs  shews  that  the  criterion  of  the  equilibrium  of  a 
system  is  contained  in  the  following  statement ; — 

For  the  equilibrium  of  any  isolated  system  it  is 
necessary  and  sufficient  that  in  all  possible  variations 
of  the  state  of  the  system  which  do  not  alter  its  entropy, 
the  variation  of  its  energy  shall  either  vanish  or  be 
positive ;  or,  in  other  words,  in  all  possible  variations 
of  the  state  of  the  system  which  do  not  alter  its  energy, 
the  variation  of  its  entropy  shall  either  vanish  or  be 
negative. 

As  the  masses  of  the  constituents  of  a  system  undergoing 
chemical  change  do  not  remain  constant,  an  equation  which  is 
to  express  the  conditions  of  equilibrium  of  such  a  system  must 
take  into  account  the  changes  of  energy  produced  by  changes 

1  Amer.  Journ.  of  Sci.  and  Arts,  (3).  16.  441 ;  18,  277.  See  also  Clerk 
Maxwell,  South  Kensington  Science  Conferences  [1876]. 


CH.  II.  §189]      THERMODYNAMICAL   METHODS.  3$I 

in  the  masses  of  the  constituents.  This  is  done  by  Gibbs  by 
introducing  into  his  equations  a  term  which  represents  the 
potential  of  each  constituent.  If  an  infinitesimal  mass  of  a 
body  is  introduced  into  a  homogeneous  system  without 
disturbance  of  the  homogeneity  and  without  change  in  the 
entropy  and  volume  of  the  system,  then  the  increase  in  the 
energy  of  the  system  divided  by  the  infinitesimal  mass  of  the 
substance  added  is  the  potential  of  that  substance  in  the 
system. 

The  energy  of  the  entire  system  is  a  function  of  the 
entropy  and  the  volume  of  the  system,  and  the  masses  of 
its  constituents ;  if  the  energy  is  known  in  terms  of  these 
variables,  then  the  absolute  temperature  and  the  pressure  of 
-the  system,  and  the  potentials  of  its  constituents,  can  be 
calculated  in  terms  of  the  same  variables.  In  this  way  all 
the  independent  relations  between  the  seven  variables,  energy, 
entropy,  volume,  masses  of  constituents,  temperature,  pressure, 
and  potentials  of  constituents,  can  be  found ;  and  on  these 
relations  depend  most  of  the  properties  of  the  system,  in- 
cluding its  chemical  properties.  A  single  equation  from 
which  all  these  relations  are  deducible  is  called  by  Gibbs 
a  fundamental  equation. 

Gibbs  shews  how  such  fundamental  equations  are  found. 
He  then  applies  these  equations  to  ideal  gases,  and  then  to 
ideal  gas-mixtures,  i.e.  mixtures  of  ideal  gases  which  obey 
the  law  of  Dalton1,  and  so  he  deduces  the  conditions  of 
equilibrium  of  such  mixtures  of  gases.  Assuming  that  the 
laws  of  ideal  gas-mixtures  apply  to  cases  in  which  chemical 
change  occurs  in  the  mixtures  themselves,  at  certain  tem- 
peratures, resulting  in  the  formation  of  one  kind  of  com- 
ponents from  another  kind,  Gibbs  deduces  a  formula  for  find- 
ing the  specific  gravity  of  a  gas-mixture  from  its  temperature 
and  pressure2.  He  applies  this  formula  to  the  gas-mixtures 
obtained  by  heating  nitrogen  peroxide  (N2OJ,  phosphorus 

1  For  convenience'  sake,  Gibbs  states  this  law  in  these  terms; — "  The  pressure 
in  a  mixture  of  different  gases  is  equal  to  the  sum  of  the  pressures  of  the  different 
gases  as  existing  each  by  itself  at  the  same  temperature  and  with  the  same  value 
of  its  potential." 

2  See/tarf,  par.  205. 


382  CHEMICAL  EQUILIBRIUM.  [BOOK  II. 

pentachloride,  formic  acid,  and  acetic  acid,  and  finds  that 
the  calculated  results  agree  on  the  whole  very  well  with  the 
observed  values  for  the  specific  gravities  of  these  gases.  Hence 
it  is  probable  that  the  fundamental  equations  obtained  by 
purely  thermodynamical  reasoning  are  applicable  to  all  cases 
of  gaseous  dissociation.  But  dissociation-processes  are  in- 
stances of  chemical  equilibrium  ;  hence  it  is  to  be  expected 
that  each  of  the  classes  into  which  the  problems  of  chemical 
equilibrium  may  be  divided  has  its  appropriate  fundamental 
equation  by  the  use  of  which  a  full  thermodynamical  expla- 
nation can  be  given  of  this  class  of  cases  of  equilibrium. 
190  One  of  the  forms  in  which  the  criterion  of  stability  is 
stated  by  Gibbs  involves  the  use  of  a  certain  function,  i|r, 
which  is  defined  by  the  equation 

t  =  e-fy, 

where  e  =  energy  of  the  system,  tj  =  entropy  of  the  system, 
and  t  —  absolute  temperature;  then  equilibrium  results  when 
in  all  possible  variations  of  the  state  of  the  system  which  do 
not  alter  its  temperature,  the  variation  of  ^  either  vanishes 
or  is  positive. 

This  form  of  stating  the  criterion  of  stability  is  in  many 
cases  more  convenient  than  that  given  in  par.  189  for  deducing 
the  conditions  of  equilibrium  of  any  system.  The  meaning 
of  the  function  -\Jr  has  been  developed  by  von  Helmholtz  *  on 
lines  different  from  those  adopted  by  Gibbs.  Helmholtz 
divides  the  internal  energy  of  a  system  into  two  parts  ;  the 
free  energy  which  can  be  completely  changed  into  other  forms 
of  energy,  and  the  bound  energy  which  is  that  portion  of  the 
total  energy  required  for  establishing  the  state  of  the  system 
conditioned  by  the  entropy  of  the  system  ;  as  every  stable  state 
corresponds  to  a  maximum  entropy,  the  bound  energy  cannot 
be  changed  to  other  forms  within  the  system,  nor  without 
external  action  on  the  system.  The  bound  energy  is 
measured  by  the  difference  between  the  total  and  the  free 
energy.  Helmholtz's  free  energy  is  identical  with  Gibbs' 
function  i/r, 

1  'Die  Thermodynamik  Chemischer  Vorgange,'  Sitaber.  der  Wiss.  Akod  zu 
Berlin,  1882,  also  Helmholtz's  Wissenschoftliche  Abhandlungen,  2.  958. 


CH.  II.  §  IQO,  191]  THERMODYNAMICAL   METHODS.  383 

All  the  properties  of  a  system  may  be  represented  in 
equations  as  functions  of  the  free  energy  of  the  system. 
Such  equations  have  been  deduced  for  some  of  the  chemical 
properties  of  a  system  in  equilibrium,  e.g.  for  dissociation- 
processes  of  different  orders  of  complexity,  and  for  reciprocal 
actions  when  some  members  of  the  system  are  gases  and  some 
solids.  These  equations  lead  to  results  identical  with  those 
already  obtained  by  the  use  of  the  empirical  method  of 
Guldberg  and  Waage x. 

The  transformability  of  the  chemical  energy  of  a  system 
into  other  forms  of  energy  is  measured  by  the  free  energy, 
and  not  by  the  total  energy,  of  the  system.  For  instance, 
the  energy  obtained  from  a  chemical  reaction  in  the  form  of 
heat  does  not  measure  the  electrical  energy  obtainable  from 
the  same  system  ;  for  the  latter  is  obtained  by  the  transforma- 
tion of  the  free  energy  only  and  not  of  the  total  energy.  So 
also  in  a  chemical  change,  the  direction  of  the  change  is 
determined  by  the  free  energy  of  the  changing  system,  and 
this  is  not  measured  by  finding  the  quantity  of  the  heat 
produced  in  the  change. 

II  One  of  the  consequences  of  the  general  criterion  of  stability 
deduced  from  the  second  law  of  thermodynamics  is,  that 
Berthelot's  so-called  '  law  of  maximum  work '  is  inaccurate. 

Berthelot's  law  asserts  that  'every  chemical  change  accom- 
plished without  the  addition  of  energy  from  without  tends  to  the 
formation  of  that  body  or  system  of  bodies  the  production  of 
which  is  accompanied  by  the  development  of  the  maximum 
quantity  of  heat.'2 

Now  a  system  is  in  equilibrium  when  its  entropy  has 
attained  the  maximum  value  possible  under  the  conditions. 
But  inasmuch  as  entropy  is  measured  by  a  quantity  of  heat 
divided  by  a  temperature,  it  is  only  at  the  absolute  zero 
of  temperature  that  dS  =  dQ  (S  =  entropy,  Q  =  quantity  of 
heat);  hence  it  is  only  at  the  absolute  zero  that  thermal 

1  See  Ostwald,  Lekrbuch,  2.  716 — 724;  also  P.  Duhem,  '  Le  potentiel  thermo- 
dynamique'  [Paris,  1886 — 7]. 

2  See  ante,  Book  I.,  par.  133  for  a  discussion  of  the  practical  applications 
of  this  statement. 


384  CHEMICAL   EQUILIBRIUM.  [BOOK  II. 

changes  directly  measure  changes  of  entropy.  When  a 
chemical  change  is  accompanied  by  the  production  of  much 
heat,  and  the  change  occurs  at  a  low  temperature,  the  thermal 
change  will  roughly  measure  the  entropy-change ;  therefore 
if  such  a  change  be  possible  it  will  occur.  But  if  the  quantity 
of  heat  produced  in  a  chemical  process  is  small,  the  entropy- 
change  which  the  system  undergoes  may  be  largely  con- 
ditioned by  changes  other  than  the  thermal  change.  Indeed 
in  some  cases  heat  may  be  lost  to  the  system,  and  yet  the 
total  change  in  the  entropy  may  be  positive ;  in  such  cases 
chemical  change  will  occur  with  the  disappearance  of  heat, 
because  the  decrease  in  the  entropy  of  the  system  caused  by 
the  loss  of  heat  will  be  more  than  balanced  by  the  increase 
in  the  entropy  caused  by  the  changes  of  state  which  the 
system  undergoes. 

Such  chemical  changes  are  analogous  to  the  physical  change 
of  water  in  vacua  into  water-gas ;  in  this  case  the  water  loses 
heat,  but  the  loss  of  entropy  thus  suffered  is  more  than 
balanced  by  the  gain  of  entropy  accompanying  the  change 
from  liquid  to  gaseous  water. 

So  far  as  the  law  of  entropy  has  been  applied  to  chemical 
processes,  it  has  led  to  the  same  conclusions  regarding  the 
equilibrium  of  chemical  systems  as  have  been  gained  by  the 
application  of  the  law  of  mass-action.  The  general  con- 
ception of  chemical  change  which  is  given  by  both  methods 
of  investigation  is  that  of  a  system  attaining  equilibrium  as 
the  result  of  processes  occurring  in  opposite  directions.  Ac- 
cording to  van't  Hoff1,  the  directions  of  chemical  processes 
which  result  in  equilibrium  vary  with  variations  of  tempera- 
ture in  such  a  way  that  the  lower  the  temperature  the  more 
is  equilibrium  established  with  the  production  of  heat,  but  the 
change  can  occur  in  one  direction  only  at  the  absolute  zero. 
Berthelot's  '  law '  would  then  hold  good  for  the  limiting  case 
that  the  change  should  occur  at  —  273°.  As  the  temperature 
at  which  most  chemical  changes  occur  is  not  very  high  very 
many  changes  are  accompanied  by  production  of  heat. 

Berthelot's  '  law  of  maximum  work '  is  the  modern  form 

1  Dynanrique  chimique,  153. 


CH.  II.  §§191,192]    MOLECULAR  METHODS.  385 

assumed  by  the  old  Bergmannic  view  of  affinity.  Berthelot, 
like  Bergmann,  regards  chemical  affinity  as  acting  in  one 
direction  only.  But  the  outcome  of  all  recent  investigation 
is  to  negative  this  view,  and  to  confirm  the  conception  of 
affinity  which  was  first  clearly  introduced  into  chemistry  by 
the  great  French  naturalist  Berthollet. 


SECTION  IV.     Molecular  methods  applied  to 
chem  ical  equilibrium. 

192  In  185 1  Williamson1  suggested  that  the  amount  of  chemical 
change  which  occurs  between  two  interacting  bodies  is  de- 
pendent on  the  velocities  of  the  atomic  interchanges  which 
take  place  between  the  molecules  of  the  bodies.  He  extended 
this  conception  to  molecules  all  of  the  same  kind,  and  con- 
cluded that  "  in  an  aggregate  of  molecules  of  any  compound 
there  is  an  exchange  continually  going  on  between  the  elements 
which  are  contained  in  it."  He  supposed,  for  instance,  that 
in  a  vessel  filled  with  hydrochloric  acid  the  molecules  HC1 
are  continually  exchanging  hydrogen  and  chlorine  atoms ; 
if  then  a  solution  of  copper  sulphate  is  added  to  hydrochloric 
acid  "  the  hydrogen  does  not  merely  move  from  one  atom  of 
chlorine  to  another,  but  in  its  turn  also  replaces  one  atom 
of  copper,  forming  chloride  of  copper  and  sulphuric  acid." 
When  one  product  of  a  chemical  change  is  insoluble  it  is 
removed,  and  so  almost  the  whole  of  one  of  the  original 
substances  is  decomposed  ;  but  if  all  the  products  remain  in 
solution,  the  atomic  interchanges  proceed  in  both  directions 
and  equilibrium  is  thus  established. 

In  1857  Clausius2  developed  a  conception  similar  to 
that  put  forward  by  Williamson,  and  applied  it  especially 
to  explain  the  phenomena  of  electrolysis.  He  supposed  that 
the  movements  of  the  molecules  of  a  liquid  result  in  the 
production  of  such  a  condition  of  some  of  the  molecules  as 
makes  these  molecules  ready  to  exchange  their  constituent 
parts.  As  increasing  temperature  is  equivalent  to  increasing 

1  C.  S.  Journal,  4.  no;  229.     Also  Phil.  Mag.  (3).  37.  350. 

2  Pogg-  Ann.  101.  338. 

M.C.  25 


386  CHEMICAL  EQUILIBRIUM.  [BOOK  II. 

the  kinetic  energy  of  the  molecules,  increase  of  temperature 
will  bring  about  further  separation  of  molecules  into  parts, 
and  will  therefore  increase  the  chances  of  the  exchange  of 
parts  of  molecules. 

Clausius'  hypothesis  postulates  differences  in  the  conditions 
of  the  molecules  forming  a  liquid  compound  at  any  specified 
temperature,  and  asserts  that  some  of  the  molecules  will 
be  more  ready  to  exchange  parts  than  others 1. 

Pfaundler2,  in  1867  and  1874,  developed  the  hypothesis  of 
Clausius  and  Williamson  and  applied  it  to  many  chemical 
reactions,  and  more  particularly  to  explain  the  phenomena  of 
dissociation 8. 

Pfaundler  considers  the  motion  of  agitation  of  the  molecules 
of  a  gas,  and  also  the  motion  of  parts  of  the  molecules ;  ac- 
cording to  the  kinetic  theory  of  gases,  the  sum  of  the  kinetic 
energies  due  to  these  two  motions  is  constant  at  a  constant 
temperature,  and  the  sum  of  each  is  constant,  but  the  two 
motions  may  be  very  differently  distributed  among  the  indi- 
vidual molecules.  The  results  of  collision  between  two 
molecules  will  depend  on  the  ratio  between  the  energy  of 
agitation,  and  the  energy  of  rotation  of  the  parts,  of  the 
molecules ;  the  limiting  cases  are  when  both  energies  are 
at  a  maximum,  or  both  are  at  a  minimum,  or  either  is  at 
a  maximum  compared  with  the  other  at  a  minimum. 
193  Guldberg  and  Waage4,  in  1879,  brought  the  hypothesis  of 
chemical  action  being  due  to  differences  in  the  states  of  the 
molecules  of  a  gas  or  liquid  into  a  form  in  which  it  could 
be  quantitatively  applied.  Let  the  molecules  of  two  substances 
which  react  chemically  with  one  another  be  represented  by 
A  and  B;  let  these  molecules  be  composed  of  the  atoms 
(or  atomic  groups)  aa,  and  bby  respectively,  performing  certain 
vibrations  within  the  molecules  A  and  B.  At  certain  points 
in  these  vibrations  the  atoms  aa  on  the  one  hand,  and  the 

1  For  some  account  of  the  applications  of  the  hypothesis  of  Clausius,   see 
post,  par.  204. 

2  Fogg.  Ann.  131.  55  et  seq.  (especially,  pp.  66—71);  do.  Jubelbd.  182. 

3  See  Section  v.  of  the  present  Chapter. 

4  Journal  fur  prakt.  CAenu'e,  (2).  19.  75. 


CH.  II.  §§193,  194]    MOLECULAR   METHODS.  387 

atoms  bb  on  the  other  hand,  will  be  so  far  separated  from  one 
another  that  the  attraction  between  them  will  be  very  small ; 
a  molecule  the  atoms  of  which  are  in  this  condition  will  be 
ready  to  undergo  chemical  change.  Suppose  that  a  molecule 
A  comes  near  to  a  molecule  B  at  the  moment  when  each  is 
ready  to  undergo  change,  chemical  action  will  occur  with  the 
production  of  two  new  molecules,  C,  each  composed  of  the 
atoms  ab.  If  the  number  of  molecules  of  A  which  are  in  this 
condition  of  readiness  to  undergo  change  be  a,  the  total 
number  of  molecules  of  A  in  unit  volume  of  the  system 
being  p,  and  if  the  number  of  molecules  of  B  ready  to 
undergo  change  be  b,  the  total  number  of  molecules  of  B 
being  g,  then  the  frequency  of  collision  of  the  molecules 
which  are  ready  to  change  will  be  represented  by  the  product 
(apbq\  and  the  velocity  of  formation  of  the  new  molecules,  C, 
will  be  represented  by  $apbq,  where  <j>  is  a  velocity-coefficient 
which  depends  on  the  temperature  and  the  chemical  nature 
of  the  substances  A  and  B.  The  nature  of  this  dependence 
must  be  experimentally  determined.  An  expression,  similar 
to  that  given,  can  be  found  for  the  velocity  of  re-formation  of 
A  and  B;  and  hence  the  amounts  of  A,  B,  and  C,  which  are 
present  when  equilibrium  is  attained  can  be  calculated  for  any 
initial  state  of  the  system. 

The  equation  of  equilibrium  thus  found  is 
$apbq  =  tfa'b'p'q'. 

If  k  is  put  as  =  $ab  and  k'  as  =  fy'a'b',  the  equation  becomes 
kpq  =  k'p'q'. 

This  equation  is  essentially  the  same  as  that  which 
Guldberg  and  Waage  arrived  at  by  the  use  of  methods 
which  did  not  involve  any  theory  of  the  structure  of  matter. 
We  have  already  traced  the  development  and  applications 
of  this  equation  of  equilibrium  \ 

194  J-  J-  Thomson2  has  given  a  general  conception  of  chemical 
equilibrium  in  terms  of  the  vortex-atom  theory  of  the  structure 
of  matter. 

1  Ante,  pars.  172 — 186. 

2  On  the  motion  of  vortex  rings.     The  Adams  Prize  Essay  for  1882.     (See 
also  Phil.  Mag.  (5).  15.  427;  17.  233;  18.  233.) 

25—2 


388  CHEMICAL   EQUILIBRIUM.  [BOOK  II. 

A  compound  molecule  of  a  gas  is  regarded  by  this  theory 
as  consisting  of  two,  or  more,  vortex  rings.  This  united  vortex 
ring  will  separate  into  its  parts  when  subjected  to  a  disturbing 
influence,  such  as  the  action  due  to  other  vortex  rings  in  the 
neighbourhood.  The  theory  thus  leads  to  a  conception  of 
chemical  combination  closely  resembling  that  enunciated  by 
Williamson,  Clausius,  and  Pfaundler.  But  for  a  compound 
gas  to  be  more  than  a  mere  mixture  of  elementary  gases  it  is 
necessary  that  'the  mean  time  during  which  an  atom  is  paired 
with  another  of  a  different  kind,  which  we  shall  call  the  paired 
time,  should  be  large,  compared  with  the  time  during  which  it 
is  alone  and  free  from  other  atoms,  which  we  shall  call  the 
free  time'  (loc.  cit.  p.  115). 

The  ratio  of  paired  to  free  time  will  be  diminished  by  any 
disturbance  to  which  the  gas  is  subjected;  when  the  diminu- 
tion is  carried  past  a  certain  amount,  the  gas  is  decomposed. 

Now  'the  pairing  of  two  atoms is  attended  by  a  large 

increase  in  the  translatory  energy;'  but  as  these  atoms  are 
only  paired  for  a  time,  '  the  whole  increase  in  the  translatory 

energy  of  a  large  number  of  molecules  will  depend on 

the  ratio  of  the  paired  to  the  free  times'  of  the  vortex 
atoms  which  form  the  molecules  of  the  substance  (loc.  cit. 
p.  1 1 6).  The  value  of  this  ratio  in  the  case  of  an  elementary 
gas  will  to  a  great  extent  condition  the  chemical  properties  of 
that  gas  ;  it  will  also  determine  whether  chemical  combination 
shall  or  shall  not  occur  between  two  gases,  and  if  it  occurs,  it 
will  fix  the  proportions  between  the  amounts  of  the  various 
compounds  produced.  An  elementary  gas  will  readily  enter 
into  chemical  combination,  only  when  the  ratio  of  free  to 
paired  time  is  larger  for  the  molecule  of  the  element,  than  for 
that  of  the  compound  produced.  The  value  of  the  ratio  in 
question  may  therefore  afford  a  measure  of  the  relative 
affinities  for  each  other  of  the  atoms  of  various  compound 
molecules. 

This  conception  of  chemical  change  is  applied  by  Thomson 
chiefly  to  processes  of  dissociation  ;  the  results  obtained  will 
be  briefly  considered  in  the  next  section. 


CH.  II.  §§  194,  195]  DISSOCIATION.  389 

SECTION  V.     Dissociation. 

195  Certain  changes  brought  about  by  heat  and  resulting  in 
the  formation  of  systems  in  equilibrium  are  classed  together 
under  the  common  term  dissociation. 

By  this  term  is  meant  a  change  from  one  chemical  system 
to  another  simpler  system  which  change  is  caused  by  heat 
and  is  reversible.  The  composition  of  the  constituents  of  the 
simpler  system  is  less  complex  than  that  of  the  bodies  which 
form  the  original  system.  At  least  one  member  of  the  simpler 
system  is  gaseous  under  the  conditions  of  the  experiment.  The 
resolution  of  the  compound  N2O4  into  2NO2,  or  of  C6HnBr 
into  C5H10  and  HBr,  or  of  CaCO3  into  CO2  and  CaO,  and  the 
subsequent  re-formation  of  the  original  compound  on  cooling 
the  products  of  each  action,  are  examples  of  dissociation. 

In  the  change  of  N2O4  into  2NO2,  both  the  original  body 
and  that  formed  by  heating  the  original  are  gases ;  hence  the 
change  in  question  must  be  accompanied  by  a  decrease  in  the 
spec.  grav.  of  the  gas.  If  it  has  been  proved  that  the  only 
change  which  occurs  when  N2O4  is  heated  is  the  gradual  dis- 
appearance of  the  N2O4  with  the  simultaneous  production  of 
2NO2,  then  the  amount  of  this  change  which  occurs  at  any 
specified  temperature  and  pressure  can  be  calculated  from 
observations  of  the  spec.  grav.  of  the  gas  at  that  temperature 
and  pressure. 

There  are  cases  where  a  gas  becomes  specifically  lighter 
as  temperature  increases,  without  our  being  able  to  demon- 
strate by  conclusive  experiments  that  the  decrease  in  spec, 
grav.  is  accompanied  by  dissociation  of  the  gas  into  simpler 
components.  For  instance,  the  spec.  grav.  of  the  gas  ob- 
tained by  heating  ammonium  chloride  is  considerably  less 
than  the  value  calculated  on  the  assumption  that  this  gas 
consists  of  the  compound  NH4C1;  and  the  spec.  grav. 
decreases  as  temperature  rises,  until  at  about  350°  it  is  very 
nearly  identical  with  that  calculated  for  a  mixture  of  equal 
volumes  of  NH3  and  HC1  (calcd.  =  -93;  observed  =  ro).  We 
seem  justified  in  considering  the  gas  obtained  by  heating 
NH4C1  to  350°  to  be  a  mixture  of  equal  volumes  of  NH3 


390  CHEMICAL  EQUILIBRIUM.  [BOOK  II. 

and  HC1,  with  perhaps  a  little  unchanged  NH4C1,  although 
there  is  no  absolutely  conclusive  experimental  demonstration 
that  this  is  so.  In  support  of  this  conclusion  may  be  men- 
tioned Pebal's1  proof  that  if  the  vapour  obtained  by  heating 
ammonium  chloride  is  diffused  through  a  porous  septum  the 
diffusate  contains  considerable  quantities  of  free  ammonia. 

Another  instance  of  this  kind  is  presented  by  acetic  acid 
vapour.  Ramsay  and  Young2  have  shewn  that  this  vapour 
becomes  specifically  heavier  by  increasing  pressure  at  any 
temperature  or  by  decreasing  temperature  at  any  pressure. 
They  contrast  this  behaviour  with  that  of  the  vapour  of 
alcohol  and  ether,  which  are  almost  certainly  non-dissociable 
bodies;  the  spec,  gravities  of  these  vapours  increase  as  tempera- 
ture is  decreased,  at  a  fixed  pressure,  until  a  certain  value  is 
reached  after  which  decrease  of  temperature  does  not  change 
the  spec,  gravities.  The  conclusion  to  be  drawn  from  these 
observations  is  that  acetic  acid  vapour  at  low  temperatures 
is  probably  composed  for  the  most  part  of  molecules  which 
are  more  complex  and  heavier  than  those  which  chiefly 
compose  this  vapour  at  high  temperatures,  and  that  the 
former  are  dissociated  into  the  latter  as  temperature  rises. 

When  the  spec.  grav.  of  the  gas  obtained  by  heating  a 
definite  compound  decreases  as  temperature  increases,  and 
reverts  to  its  original  value  when  the  temperature  falls  to 
its  initial  value,  and  when  the  change  of  spec.  grav.  quanti- 
tatively corresponds  with  a  change  of  composition  which  can 
be  presented  in  a  definite  manner,,  and  which  is  perfectly 
justifiable  on  other  grounds,  and  is  the  only  change  of 
composition  which  will  explain  the  observed  variations  of 
spec,  grav.,  we  are  justified  in  regarding  the  variations  of 
spec.  grav.  as  indications  and  measures  of  the  change  of 
composition.  For  if  we  do  not  thus  regard  these  variations 
of  spec,  grav.,  then  we  must  regard  the  gases  in  question 
as  having  abnormal  coefficients  of  expansion3,  and  coefficients 
so  abnormal  as  to  demand  a  complete  revision  of  our  con- 

1  Annalen.  126.  193. 

2  C.  S.  Journal,  Trans,  for  1886.  790;  Phil.  Mag.  (5).  23.  129. 

3  Deville  and  Troost,  Compt.  rend.  64.  237;  91.  54;  Berthelot,  do.  91.  77. 


CH.  II.  §§  195,  196]  DISSOCIATION.  39! 

ceptions  regarding  the  relations  between  the  volumes  of  gases 
and  changes  of  temperature.  For  instance,  we  should  have 
to  admit  that  the  coefficients  of  expansion  of  such  gases  as 
ammonium  chloride,  phosphorus  pentachloride,  &c.,  which 
gases  are  generally  regarded  as  undergoing  dissociation  on 
heating,  increase  as  temperature  rises,  but  increase  rapidly 
until  a  maximum  is  reached  and  then  increase  slowly.  But 
there  is  no  conclusive  proof  that  the  coefficients  of  expansion 
of  any  gases  change  in  this  way ;  and  moreover  it  has  been 
experimentally  shewn  that  the  coefficients  of  expansion  of 
the  following  elementary  and  compound  gases  are  practically 
unchanged  for  a  very  large  range  of  temperature ;  hydrogen, 
oxygen,  nitrogen,  sulphur,  tellurium,  mercury,  carbon  di- 
oxide, hydrogen  chloride,  arsenious  oxide l. 

196  The  so-called  abnormal  vapour-densities  of  various  gases 
are  at  once  explained  if  we  suppose  that  the  gases  in  question 
are  dissociated  on  heating,  and  that  therefore  the  observed 
vapour-densities  are  the  spec,  gravities  of  mixtures  and  not  of 
single  gases.  For  instance  the  composition  of  sulphuric  acid 
is  undoubtedly  expressed  by  the  formula  H2SO4 ;  if  this  com- 
pound were  gasified  the  spec.  grav.  of  the  gas  must  be  49 
times  that  of  hydrogen  (H2SO4  =  98);  but  the  spec.  grav. 
of  the  gas  obtained  by  vaporising  sulphuric  acid  is  con- 
siderably less  than  49,  and  the  spec.  grav.  decreases  as 
temperature  rises  until  at  about  400°  the  value  obtained  is 
24-5.  These  results  are  at  once  explained  by  supposing  that 
the  compound  H2SO4  is  dissociated  into  a  mixture  of  equal 
volumes  of  the  two  gaseous  compounds  SO3  and  H2O,  as  the 
spec.  grav.  of  such  a  mixture  would  be  24-5  times  that  of 
hydrogen.  As  the  variations  in  the  spec.  grav.  of  the  vapour 
obtained  by  heating  sulphuric  acid  as  temperature  increases 
and  decreases  are  exactly  similar  to  the  variations  observed 
in  the  spec,  gravities  of  gases  which  undoubtedly  undergo 
dissociation,  we  are  justified  in  saying  that  the  expression 
abnormal  vapour-density  of  sulphuric  acid  should  not  be  used, 
because  the  vapour  is  not  sulphuric  acid  but  is  a  mixture  of 
two,  and  probably  three,  gases  in  variable  proportions.  The 

1  V.  Meyer,  Ber.  13.  2022;  see  also  Langer  and  Meyer,  Ber.  18.  Ref.  133. 


392  CHEMICAL   EQUILIBRIUM.  [BOOK  II. 

other  cases  of  so-called  abnormal  vapour  densities  cease  to 
be  abnormal  when  we  are  prepared  to  admit  the  occurrence  of 
dissociation. 

197  The  amount  of  dissociation  which  any  body  undergoes 
depends   upon  the   temperature,  and   also   on    the   pressure. 
As   the   body  is   heated,  temperature  rises,  and  the  rate  of 
dissociation  increases  until  a  maximum  is  reached,  after  which 
the  rate  of  dissociation  decreases  until  the  change  is  completed; 
on  cooling  the  products  of  dissociation  in  contact  with  each 
other,  this  process  is  reversed.     If  pressure  and  temperature 
are  kept  constant,  the  system  composed  of  the  original  body 
and  the  products  of  dissociation  settles  down  into  equilibrium, 
which  is  disturbed  either  by  changing  the  temperature  or  the 
pressure,  although  in  some  cases  change  of  pressure  does  not 
affect   the   equilibrium  nearly  so  much  as  it  does  in  other 
cases1. 

The  pressure  at  which  equilibrium  is  attained  for  any 
specified  temperature  is  usually  called  the  equilibrium-pressure 
for  that  temperature2. 

198  Consider  the  effect  of  heat  on  a  quantity  of  ammonium 
chloride   enclosed    in   a   vacuous   vessel    connected   with   an 
air-pump  and  a  manometer.     As  the  solid  is  heated,  vapour 
is  produced,  and  this  vapour  consists  of  equal  volumes  of 
ammonia  and  hydrogen  chloride  possibly  mixed  with  small 
quantities  of  ammonium  chloride  gas.     This  change  proceeds, 
with  constant  rise  of  temperature,  and  increase  of  pressure  in 
the  interior  of  the  vessel.     Now  let  the  temperature  be  kept 
constant,  say  at  350°,  dissociation  proceeds  until  the  pressure 
of  the  gases  in  the  vessel  attains  a  certain  amount  when  the 
process  of  dissociation  stops,  and  equilibrium  is  established 
between  the  three  bodies,  ammonium  chloride,  ammonia,  and 
hydrogen  chloride.     Now  let  temperature  be  raised  through 
a  definite  interval,  say  to  400°;  dissociation  proceeds,  more 
ammonia  and  hydrogen  chloride  are  produced,  and  pressure 
increases  until  it  reaches  a  limit  whereat  the  system  again 
attains    equilibrium.     Now   let   a   portion    of    the   gases   be 

1  See  next  page. 

2  The  terms  equilibrium-tension,  and  tension  of  dissociation  are  also  used. 


CH.  II.  §§197,  198]  DISSOCIATION.  393 

pumped  out  of  the  vessel,  temperature  being  maintained  at 
400°;  pressure  falls,  dissociation  begins  and  proceeds  until 
the  former  pressure  is  reached.  Now  let  temperature  be 
decreased,  say  to  350° ;  combination  of  ammonia  and 
hydrogen  chloride  begins  and  pressure  falls,  and  this  pro- 
ceeds until  a  new  state  of  equilibrium  is  attained. 

This  is  a  typical  and  simple  case  of  dissociation  ;  one 
definite  body  is  resolved  into  two  others  and  these  again 
recombine  to  form  the  original  body.  In  this  instance  the 
amount  of  dissociation  is  increased  either  by  increasing  the 
temperature  at  a  constant  pressure,  or  by  lowering  the  pressure 
at  a  constant  temperature. 

Now  consider  the  effect  of  heat  on  a  mixture  of  the  two 
gases  hydrogen  and  iodine1.  Let  a  mixture  of  equal  volumes 
of  these  gases  be  maintained  at  440°,  and  let  the  pressure  be 
kept  at  about  six  atmos. ;  combination  occurs  between  the 
gases  with  production  of  hydrogen  iodide,  and  this  proceeds 
until  (after  about  an  hour)  the  system  attains  a  state  of 
equilibrium  whereat  24  per  cent,  of  the  hydrogen  originally 
present  remains  uncombined  with  iodine.  Now  let  the 
pressure  be  decreased  to  2  atmos.,  then  to  I  atmo.,  and  then 
to  380  mm.,  temperature  remaining  at  440° ;  the  state  of  equi- 
librium is  practically  unchanged,  the  amount  of  uncombined 
hydrogen  varying  only  very  slightly  from  24  per  cent,  of  the 
amount  originally  present.  Now  let  the  temperature  be  de- 
creased to  350°,  the  pressure  remaining  constant,  a  new  state 
of  equilibrium  is  attained,  but  more  slowly  than  at  the  higher 
temperature,  and  this  is  practically  unchanged  if  the  pressure 
is  varied  from  4  atmos.  to  760  mm. 

But  although  the  final  state  of  equilibrium  of  a  mixture  of 
equal  volumes  of  hydrogen  and  iodine  at  350°  or  440°  is 
almost  independent  of  pressure,  yet  the  rate  at  which  that 
equilibrium  is  attained  at  these  temperatures  varies  almost 
directly  as  the  pressure. 

In  this  instance  we  have  probably  a  more  complex  oc- 
currence than  the  change  of  ammonium  chloride  into  ammonia 
and  hydrogen  chloride. 

1  Lemoine,  Ami.  Cliiin.  Phys.  (5).  12.  145;  26.  289,  especially  pp.  304 — 344. 


394  CHEMICAL   EQUILIBRIUM.  [BOOK  II. 

199  Now  consider  a  case  wherein  a  solid  is  dissociated  into 
another  solid  and  a  gas.  Let  calcium  carbonate  be  heated  in 
a  vacuous  vessel  connected  with  an  air-pump  and  a  manometer. 
The  change  which  occurs  may  be  represented  thus 

i  -;rCaCO. 


Let  the  temperature  be  kept  constant  ;  carbon  dioxide 
accumulates  until  the  pressure  becomes  constant,  and  the 
system  remains  in  equilibrium.  At  860°  the  equilibrium- 
pressure  is  8  1  mm.  and  at  1000°  it  is  520  mm.  Now  let 
pressure  be  diminished  by  removing  some  of  the  carbon 
dioxide  ;  the  direct  change  proceeds  until  the  former  pressure 
is  restored  when  the  equilibrium  again  results.  If  the  tempe- 
rature is  now  decreased,  carbon  dioxide  is  absorbed,  the  reverse 
change  occurs,  and  the  pressure  falls  until  a  fresh  equilibrium 
is  attained.  The  whole  process  follows  the  same  course  as 
that  observed  in  such  a  case  as  ammonium  chloride.  Equi- 
librium is  conditioned  by  temperature  and  pressure  and  is 
independent  of  the  masses  of  the  solid  members  of  the 
system,  viz.  lime  and  calcium  carbonate. 

200  Let  us  now  consider  a  case  wherein  a  solid  and  a  gas 
react  to  produce  more  than  one  compound  which  compounds 
are  dissociated  by  heat  into  their  solid  and  gaseous  con- 
stituents. Silver  chloride  and  ammonia  combine  to  form 
two  compounds,  2AgC1.3NH3  and  AgC1.3NH3.  If  silver 
chloride  is  brought  into  contact  with  ammonia  in  an  apparatus 
wherein  temperature  and  pressure  can  be  regulated,  the  system 
which  is  formed  may  be  composed  of  the  gas  NH3  and  any 
or  all  of  the  three  solids  AgCl,  2AgC1.3NH3,  and  AgC1.3NH8. 
If  temperature  is  kept  constant  at  about  15°,  ammonia  is 
absorbed  with  decrease  of  pressure  and  the  compound 
2AgCl  .  3NH3  is  produced  ;  if  sufficient  ammonia  is  supplied 
the  system  attains  equilibrium  at  a  constant  pressure,  and  the 
only  components  of  this  system  are  2AgC1.3NH3  and  am- 
monia. By  raising  temperature  equilibrium  is  upset,  and 
pressure  increases  because  of  the  production  of  more  ammonia; 
but  at  a  definite  temperature  equilibrium  is  again  attained  ; 
this  equilibrium  is  independent  of  the  ratio  between  the 


CH.  II.  §§199,  200]  DISSOCIATION.  395 

masses  of  the  two  solid  members  of  the  system,  viz.  AgCl 
and  2AgCl  .  3NH3,  and  is  conditioned  only  by  the  temperature 
and  the  pressure. 

Suppose  equilibrium  has  been  attained  at  say  20°,  and 
that  the  system  consists  of  2AgCl.  3NH3  and  ammonia;  let 
ammonia  be  pumped  into  the  vessel  so  that  the  pressure  is  con- 
siderably increased;  formation  of  the  compound  AgCl^NH, 
begins,  and  pressure  falls  until  equilibrium  is  attained  in  the 
system  consisting  of  ;r(2AgC1.3NH3),  y  (AgC1.3NH3),  and 
^rNH3.  If  the  temperature  is  now  lowered,  more  ammonia 
is  absorbed,  more  AgC1.3NH8  is  formed,  and  pressure  con- 
tinues to  fall  until  a  new  state  of  equilibrium  is  attained. 
For  every  temperature  there  is  a  certain  pressure  whereat 
equilibrium  is  established  ;  this  equilibrium  is  independent  of 
the  ratio  between  the  masses  of  the  solid  members  of  the 
system,  viz.  2AgCl-3NH3  and  AgC1.3NH3. 

In  this  case  then  two  processes  occur  ;  dissociation  of  the 
compound  2AgC1.3NH3  into  silver  chloride  and  ammonia,  and 
dissociation  of  the  compound  AgC1.3NH3  into  2AgC1.3NH3 
and  ammonia.  The  compositions  of  the  two  systems  may  be 
represented  as 


(i) 
(2) 

In  each  case  equilibrium  is  independent  of  the  ratio  of 
x  to  y.  At  any  specified  temperature  each  system  attains 
equilibrium  at  a  definite  pressure  ;  the  differences  between  the 
equilibrium-pressures  of  the  two  systems,  at  the  same  tempe- 
rature, are  so  great  that  it  is  easy  to  study  the  relations 
between  temperature  and  pressure  on  the  one  hand  and  the 
composition  of  each  system  on  the  other  hand.  The  equi- 
librium-pressures for  the  two  systems  at  temperatures  varying 
from  6°  to  20°  are  given  in  the  following  table  1  :  — 

1  Horstmann,  Ber.  9.  749.     Isambert,  Comp.  rend.  66.  1259;  70.  456. 


396  CHEMICAL   EQUILIBRIUM.  [BOOK  II. 

Temp.  Equilibrium-pressure  in  mm. 


2AgCl.3NH3          AgCl.3NH3 

6°  22      — 

7  23-4  — 

8  24-9  432 

9  26-5  446 

10  28-2  465 

12  31-9  520 

16  40-9  653 

18  46-6  723 

20  52-6  793 

201  If  a  solid  were  changed  by  heat  into  a  series  of  other 
solids  and  a  gas,  and  if  the  equilibrium-pressures  of  the  dif- 
ferent systems  thus  produced  were  nearly  the  same  at  any 
specified  temperature,  it  would  be  impossible  to  disentangle 
the  various  processes  of  dissociation  occurring  when  such  a 
solid  was  heated,  and  to  establish  the  connexions  which 
certainly  exist  between  temperature  and  pressure  and  the 
composition  of  the  various  members  of  the  complete  system. 

Such  a  case  occurs  when  certain  hydrated  salts  are 
heated.  For  instance  copper  sulphate  forms  a  series  of 
hydrates  CuSO4.^H2O;  if  a  crystal  of  the  ordinary  hy- 
drate CuSO4.5H2O  is  heated  in  a  closed  vessel  of  such  a 
size  that  the  water  of  the  crystal  is  more  than  sufficient  to 
saturate  the  air  in  the  vessel,  water-gas  is  evolved,  and  the 
pressure  increases ;  after  a  time  the  process  stops.  If  the 
temperature  is  now  allowed  to  fall,  water  is  re-absorbed,  and 
the  pressure  decreases.  But  the  change  of  pressure  is  irre- 
gular and  a  long  time  must  elapse  before  equilibrium  is  attained. 
At  a  moderate  temperature  the  crystal  is  slowly  dehydrated, 
but  at  the  same  time  small  quantities  of  water  are  re-absorbed 
by  parts-  of  the  crystal  which  had  before  given  off  water. 
Irregularities  in  the  form  or  surface  of  the  crystal  largely  affect 
the  processes  of  dehydration  and  rehydration,  and  cause  fluc- 
tuations in  one  direction  or  the  other.  As  these  fluctuations 
are  accompanied  by  changes  of  pressure,  it  is  almost  im- 
possible to  establish  equilibrium,  at  a  specified  temperature, 
in  the  system  consisting  of  ^CuSO4+/CuSO4.5H2 


CH.II.§2Ol]  DISSOCIATION.  397 

varying  quantities  of  other  hydrates  of  CuSO4.  Several  pro- 
cesses of  dissociation  are  proceeding  simultaneously,  and  the 
equilibrium-pressure  for  any  one  of  the  dissociating  systems 
at  a  constant  temperature  is  so  nearly  the  same  as  that  for 
the  other  systems  that  the  establishment  of  an  equilibrium- 
pressure  for  the  whole  system  is  not  attained  *. 

If  hydrated  sodium  phosphate,  Na2HPO4. 12H2O,  is  heated 
in  a  closed  vessel,  water-gas  is  given  off,  and  the  pressure 
increases.  For  any  temperature  there  is  an  equilibrium- 
pressure  established  which  is  independent  of  the  relative 
amounts  of  the  dehydrated  salt  and  the  various  hydrates 
present.  This  equilibrium-pressure  is  the  same  whether  the 
salt  Na2HPO4.  I2H2O  or  a  less  hydrated  salt  than  this  is 
used,  provided  the  quantity  of  water  in  the  salt  is  more  than 
that  required  by  the  formula  Na2HPO4.  ;H2O.  If  the  salt 
Na2HPO4-7H2O  is  heated,  a  series  of  equilibrium-pressures 
is  obtained  different  from  those  pressures  which  characterise 
the  process  when  a  salt  is  used  with  any  quantity  of  water 
more  than  that  required  by  the  formula  Na2HPO4 .  7H2O  but 
not  exceeding  that  contained  in  the  salt  Na2HPO4.  I2H2O. 
The  following  numbers  represent  the  results  obtained  by 
Debray*. 

Temp.  Equilibrium-pressures 

Salt  with  7  to  12  H»O.  Salt  with  less  than  7  H2O. 

I2°'3  7-4  mm.  4-8  mm. 

16-3  8-9    „  6-9    „ 

207  14-1    „  9-4    „ 

24  -9  i8'2    „  12-9    „ 

3i  '5  30'2    „  21-3    „ 

36  -4  salt  melted  39-5    „  30-5    „ 

40  -o  50*0    „  41*2    „ 

This  process  presents  an  example  of  dissociation  of  a 
solid  body  into  solid  and  gaseous  constituents  intermediate 
in  complexity  between  that  exhibited  by  CuSO4.  5H2O  on  the 
one  hand,  and  the  pair  of  salts,  2AgC1.3NH3  and  AgC1.3NH3, 
on  the  other  hand. 

1  For  further  details   see  Naumann,  Ber,   7.  1537;  or   Ibid.   Thermochctiiie, 
1 45  —6.     See  also  Lescoeur,  Compt,  rend.  102.  1 466. 

2  Conip.  rend.  66.  195. 


398  CHEMICAL   EQUILIBRIUM.  [BOOK  II. 

202  The  relations  between  volume,  temperature,  and  pressure, 
which  accompany  the  merely  mechanical  absorption  of  a  gas 
by  a  solid  are  different  from  those  which  mark  the  formation 
of  a  dissociable  compound  of  a  gas  and  a  solid. 

The  absorption  of  ammonia  by  charcoal  may  be  con- 
trasted with  the  combination  of  ammonia  with  silver  chloride. 
In  the  latter  case  ammonia  is  absorbed  at  12°  when  the 
pressure  is  equal  to  about  3i'9  mm.,  and  absorption  continues 
at  this  temperature  and  pressure  until  the  silver  chloride  is 
changed  into  the  compound  2AgC1.3NH3;  the  process  then 
stops,  and  the  pressure  must  be  raised  to  about  520  mm. 
before  absorption  of  ammonia  again  takes  place ;  the  result 
of  the  second  process  is  the  formation  of  the  compound 
AgC1.3NH3.  Charcoal  on  the  other  hand  absorbs  ammonia 
at  all  pressures,  temperature  being  constant,  and  the  quantity 
of  the  gas  absorbed  increases  regularly  with  increase  of 
pressure. 

Palladium  absorbs  large  quantities  of  hydrogen.  When 
temperature  is  kept  constant,  the  volume  of  hydrogen  ab- 
sorbed is  constant  although  the  pressure  is  caused  to  increase 
considerably;  but  after  the  quantity  of  hydrogen  absorbed 
corresponds  approximately  to  that  required  on  the  assumption 
that  the  compound  Pd2H  has  been  formed,  the  volume  of 
hydrogen  then  absorbed  increases  largely  as  the  pressure 
increases.  In  this  case  two  processes  very  probably  occur ; 
the  first  results  in  the  formation  of  the  dissociable  compound 
Pd2H,  and  this  follows  the  ordinary  course  of  such  changes  ; 
the  second  consists  in  the  mechanical  absorption  of  hydrogen 
by  the  compound  previously  formed,  and  this  in  turn  follows 
the  ordinary  course  of  such  occurrences. 

These  instances  shew  how  observations  of  the  relations 
between  temperature  and  pressure  and  the  process  of  ab- 
absorption  of  a  gas  by  a  solid,  or  the  evolution  of  a  gas 
from  a  solid,  enable  conclusions  to  be  drawn  regarding  the 
formation  or  non-formation  of  a  compound,  or  compounds,  of 
the  gas  with  the  solid. 

203  Processes  of  dissociation  lead  to  the  production  of  chemical 
systems  in  equilibrium.    The  generalisations  which  have  been 


CH.  II.  §§  202,  203]  DISSOCIATION.  399 

made  regarding  chemical  equilibrium  hold  good  in  cases  of 
dissociation.  Let  us  consider  a  few  classes  of  dissociation- 
processes  with  the  view  of  stating  the  law  which  expresses 
the  conditions  of  dissociation  in  each  class  \ 

The  cases  presented  by  heterogeneous  systems  composed  of 
solid  and  gaseous  constituents  admit  of  more  simple  treatment 
than  those  presented  by  homogeneous  systems  all  the  members 
of  which  are  gases.  The  simplest  case  is  that  which  presents 
itself  when  a  solid  dissociates  into  another  solid  and  a  gas, 
e.g.  when  calcium  carbonate  dissociates  into  calcium  oxide 
and  carbon  dioxide. 

Assuming  the  law  of  mass-action,  it  follows  that  equi- 
librium must  result  when  the  active  masses  of  the  members 
of  the  system  bear  a  certain  constant  ratio  to  each  other. 
But  the  active  masses  of  the  solids  are  constant2;  therefore 
equilibrium  will  be  conditioned  by  the  active  mass  of  the 
gas  ;  now  the  active  mass  of  the  gas  varies  with  variations  of 
pressure  and  temperature  ;  hence  equilibrium  will  be  attained 
at  any  specified  temperature  when  the  pressure  exerted  by 
the  gas  acquires  a  certain  fixed  value,  and  this  pressure  will 
be  independent  of  the  masses  of  the  solids.  The  equation 
of  equilibrium  assumes  the  form 

cu  =  CMM'.  and  therefore  -  —  uot 
c1ul 

where  c  and  c^  are  the  velocity-constants  of  the  direct  and 
reverse  changes,  respectively,  u  —  active  mass  of  one  solid, 
«t=active  mass  of  the  other  solid,  and  «8  =  active  mass  of 
the  gas. 

This  result  is  in  keeping  with  what  we  have  already  learnt 
regarding  this  class  of  dissociation-processes. 

When  a  solid  dissociates  into  equal  volumes  of  two  gases, 
e.g.  NH4C1  to  NH3+HC1,  the  equation  of  equilibrium  is  as 
before  cu 


where  u  =  active  mass  of  original  solid,  and  ul  and  ?/2  represent 

1  Here  again  I  merely  give  a  condensed  outline  of  Ostwald's  treatment  of  this 
subject  in  his  LehHnich,  2.  670—701. 

2  Ante,  par.  170. 


4OO  CHEMICAL   EQUILIBRIUM.  [BOOK  II. 

the  active  masses  of  the  two  gases  when  equilibrium  results  ; 
hence 

cu 

-=»>»* 

tt  is  constant,  as  it  represents  the  active  mass  of  a  solid 
present  in  excess. 

Hence  when  a  solid  dissociates  into  equal  volumes  of  two 
gases  the  product  of  the  active  masses  of  the  gases  is  equal  to 
a  constant  when  equilibrium  results,  and  is  independent  of 
the  mass  of  the  solid  body. 

If  the  space  in  which  the  dissociation  proceeds  is  vacuous, 
or  contains  an  indifferent  gas,  then  wt  =  ;/2,  and 


But  if  the  space  already  contains  one  of  the  gaseous 
products  of  dissociation,  then  ul  has  not  the  same  value 
as  u2  ;  the  greater  «t  the  smaller  is  #2,  and  vice  versa;  hence 
the  amount  of  dissociation  may  be  very  much  lessened 
by  increasing  u^  or  uz  ;  but  it  cannot  be  wholly  stopped, 
because  to  make  u^  =  o,  uz  must  be  made  =  oo  . 

As  an  example  of  the  dissociation  of  a  solid  into  two 
gases  in  presence  of  an  excess  of  one  of  these  gases,  may  be 
taken  the  results  obtained  by  Isambert  on  the  dissociation 
of  ammonium  hydrosulphide  (NH4HS)  into  ammonia  and 
sulphuretted  hydrogen  in  presence  of  excess  first  of  sulphur- 
etted hydrogen  and  then  of  ammonia1. 

When  equilibrium  results,  the  product  of  the  active  masses 
of  the  two  gases  must  be  the  same  in  each  series  of  experi- 
ments at  the  same  temperature.  Hence  if  pl  and  /a  are  the 
partial  pressures  of  the  two  gases  when  neither  is  in  excess, 
and  p[  and  /,'  are  the  partial  pressures  when  sulphuretted 
hydrogen  is  in  excess,  and  //'  and  p."  are  the  partial 
pressures  when  ammonia  is  in  excess,  the  equation 

AA=A'A'=A"A;', 

must  be  realised.     Isambert's  results  shew  a  fair  agreement 

1  Comp.  rend.  92.  919  ;  94.  958. 


CH.  II.  §§  203,  204]  DISSOCIATION.  4OI 

between  the  values  which  ought  to  be  constant1.  Ostwald 
indicates  a  source  of  error  overlooked  by  Isambert.  Con- 
sidering this,  and  also  considering  the  difficulties  in  making 
accurate  measurements  of  the  partial  pressures,  the  observed 
results  must  be  regarded  as  agreeing  very  well  with  the 
calculated  results. 

If  a  solid  dissociates  into  equal  volumes  of  three  gases,  or 
into  two  volumes  of  one  gas  and  one  volume  of  another  gas, 
the  equation  of  equilibrium  becomes 

CU  =  C^UfaUi, 

provided  some  quantity  of  one  or  other  of  the  gaseous 
products  of  dissociation  is  present  in  the  space  in  which 
dissociation  occurs;  but  if  the  space  is  vacuous -or  contains 
only  an  indifferent  gas,  then 

cu  =  Cjttf, 
for  in  this  case  u1  =  uz  —  us. 

Experiments  on  the  dissociation  of  ammonium  carbamate 
by  Naumann2  shewed  that  the  equilibrium-pressure  is  inde- 
pendent of  the  mass  of  the  solid  present : — 

CO.ONH4.NH2^±CO2  +  2NHS. 

Horstmann's  experiments,  wherein  excess  of  ammonia  was 
sometimes  present  and  sometimes  excess  of  carbon  dioxide3, 
and  more  particularly  similar  experiments  by  Isambert4, 
have  shewn  that  the  product  of  the  partial  pressures  of  the 
two  gases  is  constant  at  a  constant  temperature. 

Cases  of  homogeneous  dissociating  systems  are  considered 
by  Ostwald  (loc.  cit.  693 — 698),  and  the  various  forms  are  found 
for  the  equation  of  equilibrium,  and  are  applied  particularly  to 
the  dissociation  of  nitrogen  tetroxide.  A  convenient  form 
for  the  equation  is  that  in  which  it  gives  a  method  of  cal- 
culating the  spec.  grav.  of  a  dissociating  gas  from  observations 
of  pressure  and  temperature. 

304        As  processes  of  dissociation  are  caused  by  heat  and  are 
attended  with  changes  of  energy  to  the  dissociating  systems, 

1  For  actual  numbers  see  Ostwald,  loc.  cit.  685.  2  Amialen,  187.  48. 

3  Ber.  4.  779.  4  Compt.  rend.  93.  731 ;  97.  1212. 

M.  C.  26 


402  CHEMICAL   EQUILIBRIUM.  [BOOK  II. 

it  is  necessary  to  examine  briefly  the  thermodynamical  aspects 
of  these  occurrences.  It  will  also  be  incumbent  on  us  to  glance 
at  the  explanation  of  dissociation  which  is  afforded  by  the 
molecular  and  atomic  theory. 

The  general  conception  of  a  dissociable  gas  at  a  specified 
temperature  which  is  presented  by  the  kinetic  theory  of 
gases  is  that  of  a  system  of  molecules  the  kinetic  energy  of 
some  of  .which  is  different  from  that  of  the  mean  value  of  the 
kinetic  energy  of  the  whole  number,  and  in  which  system  the 
distribution  of  the  energy  of  rotation  of  parts  of  molecules 
also  varies.  When  heat  is  expended  upon  this  system  the 
energy  of  rotation  of  the  parts  of  the  molecules  is  increased, 
and  the  kinetic  energy  of  the  molecules  is  also  increased. 
The  result  is  that  some  of  the  molecules  are  separated  into 
parts ;  as  temperature  rises  more  molecules  are  separated  ; 
but  as  the  number  of  undissociated  molecules  becomes  smaller 
the  chances  of  any  molecules  undergoing  dissociation  also 
become  smaller ;  hence  the  velocity  of  dissociation  increases, 
as  temperature  rises,  to  a  maximum,  and  then  diminishes  to  a 
minimum  when  all  the  molecules  have  been  separated  into 
parts.  Now  suppose  the  temperature  to  be  kept  constant 
at  a  certain  point  in  the  process  of  dissociation ;  some  mole- 
cules are  being  separated  into  parts,  and  this  separation  is 
accompanied  by  disappearance  of  heat ;  but  at  the  same  time 
the  translatory  energy  of  some  of  the  portions  of  molecules 
has  become  such  that  re-combination  occurs,  and  this  process 
is  attended  with  production  of  heat.  If  then  no  heat  is 
allowed  to  enter  or  leave  the  system,  the  system  will  settle 
down  into  equilibrium  when  the  number  of  molecules  which 
dissociate  in  unit  of  time  is  equal  to  the  number  which  is 
re-formed  in  the  same  time. 

205        In  par.  189  was  given  a  brief  statement  of  Willard  Gibbs' 
thermodynamical  treatment  of  chemical  equilibrium. 

A  dissociable  gaseous  system  is  one  some  of  the  con- 
stituents of  which  can  be  produced  from  the  other  con- 
stituents ;  such  a  system  will  be  in  stable  equilibrium  when 
its  energy  has  attained  the  minimum  value  possible  for  the 
entropy  and  volume  of  the  system.  An  equation  can  be 


CH.  II.  §§  204—206]  DISSOCIATION.  403 

found  for  such  a  system  connecting  the  spec.  grav.  with  the 
temperature,  pressure,  and  volume.  To  find  whether  this 
equation  holds  good  for  actual  dissociable  gaseous  systems, 
notwithstanding  the  occurrence  of  chemical  action,  Gibbs 
compares  the  spec,  gravities  of  the  gases  obtained  by 
heating  nitrogen  tetroxide  (N2O4),  formic  acid,  acetic  acid, 
and  phosphorus  pentachloride,  at  different  pressures  and 
temperatures,  with  the  spec,  gravities  calculated  by  means  of 
the  equation  deduced  for  an  '  ideal  gas-mixture  with  con- 
vertible components.'  The  equation  in  question  is 


where  Z>  =  spec.  grav.  of  the  gaseous  mixture,  Z^spec.  grav. 
of  the  less  dense  component  of  the  mixture,  t  =  temperature, 
/  =  pressure,  and  A,  B,  and  C  are  constants  to  be  determined 
experimentally  for  each  dissociable  system.  The  observed 
results  agree  very  closely  with  the  calculated  numbers  in  most 
cases  ;  but  some  discrepancies  are  observed,  especially  in  the 
case  of  phosphorus  pentachloride. 

Gibbs  concludes  his  paper  with  these  words  ;  — 

"  The  constants  of  these  equations  are  of  course  subject  to  correction 
by  future  experiments,  which  must  also  decide  the  more  general  question, 
in  what  cases,  and  within  what  limits,  and  with  what  degree  of  approxi- 
mation, the  actual  relations  can  be  expressed  by  equations  of  such 
form." 

106  A  very  brief  sketch  was  given  in  par.  194  of  the  appli- 
cations to  chemical  equilibrium  of  the  vortex-atom  theory  of 
matter  by  J.  J.  Thomson. 

The  mean  time  during  which  an  atom  is  paired  with 
another  of  a  different  kind  is  called  the  paired  time  ;  and  the 
mean  time  during  which  the  vortex-ring  atom  vibrates  alone 
and  unpaired  is  called  the  free-time.  The  conditions  which 
determine  the  ratio  of  paired  to  free  time  in  a  dissociable  gas 
will  determine  the  amount  of  dissociation  in  that  gas.  The 
theory  gives  a  means  of  investigating  the  effect  of  a  dis- 
turbing influence,  such  as  the  action  of  heat,  light,  or  electricity, 
or  of  other  vortex-rings  in  the  neighbourhood,  on  two  vortex- 

26—2 


404  CHEMICAL  EQUILIBRIUM.  [BOOK  II. 

atoms.  Whether  the  effect  shall  be  to  separate  the  atoms, 
or  to  make  the  connexion  between  them  stronger,  depends  on 
the  direction  in  which  the  vortex-rings  are  moving.  If  they 
are  moving  in  the  same  direction  with  different  velocities  the 
effect  of  the  disturbance  will  be  to  make  them  hold  more 
firmly  together  ;  but  if  they  are  moving  in  opposite  directions 
with  different  velocities  the  effect  of  the  disturbance  will  be 
to  separate  the  rings. 

Thomson  then  considers  the  conditions  under  which  the 
ratio  of  paired  to  free  time  is  so  reduced  that  the  gas  separates 
into  its  constituents.  He  considers  cases  of  various  degrees  of 
complexity,  beginning  with  that  of  an  elementary  gas  the 
molecules  of  which  are  diatomic.  He  shews  how  an  equation 
is  arrived  at  for  such  a  gas  whereby  the  ratio  of  the  number 
of  free  atoms  to  the  number  of  molecules  at  any  time  may  be 
determined.  This  equation  may  be  expressed  as  an  equation 
giving  the  vapour-density  of  the  dissociated  gas;  and  the 
results  calculated  by  it  can  then  be  compared  with  the  ex- 
perimentally determined  results.  Further,  this  form  of  the 
equation  varies  according  as  it  is  assumed  that  the  dissoci- 
ation is  produced  by  collisions  between  the  molecules,  or  by 
some  external  agency  such  as  heat,  light,  or  electricity.  In 
the  simple  case  of  iodine  vapour  "  if  the  dissociation  were  due 
to  the  collisions  of  the  particles,  then  the  paired  time  would 
vary  inversely  as  the  number  of  collisions,  and... dissociation 
would  be  the  same  at  all  pressures."  But  the  dissociation-  of 
iodine  vapour  is  dependent  on  the  pressure,  hence  the  dis- 
sociation is  probably  not  due  to  collisions  between  the  mole- 
cules, but  rather  to  the  action  of  some  external  agency. 
In  considering  the  change  of  gaseous  hydriodic  acid  into 
iodine  and  hydrogen  it  is  shewn  that  the  amount  of  the 
change,  at  a  given  temperature,  should  be  much  less  de- 
pendent on  pressure  than  in  the  case  of  iodine  vapour.  This 
conclusion  follows  whether  the  change  is  regarded  as  the  effect 
of  collisions  between  the  molecules,  or  as  the  effect  of  an 
external  agency.  The  experimental  results  obtained  by 
Lemoine1  confirm  Thomson's  theoretical  deduction.  Other 

1  See  The  Elements  of  Thermal  Chemistry,  par.  160. 


CH.  II.  §§  2O6  —  2O8]          DISSOCIATION.  405 

cases  are  considered  in  the  paper  referred  to,  and  equations 
are  deduced  whereby  the  conditions  which  determine  the 
ratio  of  paired  to  free  time,  and  therefore  determine  the 
amount  of  dissociation,  may  be  obtained. 
07  Dissociation-processes  come  under  the  laws  which  express 
the  conditions  of  chemical  equilibrium.  In  a  chemical  de- 
composition we  have  doubtless  collisions  occurring  between 
different  kinds  of  molecules  resulting  in  the  shattering  of 
these  molecules  and  the  formation  of  molecules  of  other 
kinds.  The  theoretically  simplest  case  of  dissociation  occurs 
when  the  molecules  of  one  kind  of  matter  are  separated  into 
parts  by  the  action  of  heat  without  the  occurrence  of  reactions 
between  the  parts  of  the  molecules;  such  a  separation  probably 
occurs  in  the  dissociation  of  the  molecule  I2  into  the  atoms 
I  +  I.  In  the  dissociation  of  molecules  of  the  composition  HI 
into  the  molecules  H2  and  I2,  it  is  probable  that  two  actions 
occur,  one  being  represented  by  the  equation 


and  the  other  by  the  equation 


406  CHEMICAL    EQUILIBRIUM.  [BOOK    II. 

Chemical  change  then  follows  the  same  laws  as  other  classes 
of  physical  occurrences;  the  differences  between  chemical 
and  physical  occurrences  are  differences  of  degree  and  not  of 
kind. 

It  is  important  to  notice  that  although  the  thermody- 
namical  treatment  of  chemical  equilibrium  provides  for  the 
consideration  of  the  influence  of  temperature,  nevertheless 
there  has  not  as  yet  been  any  thorough  examination  of  the 
effect  of  variations  of  temperature  on  the  velocities  of 
chemical  changes. 

Some  chemical  occurrences  seem  to  be  independent  of 
temperature,  while  others  are  largely  conditioned  by  changes 
in  this  variable.  Various  formulse  have  been  given  for  shew- 
ing the  connexion  between  temperature  and  rate  of  change, 
but  none  is  altogether  satisfactory1. 

In  the  earlier  statement  of  the  equation  of  equilibrium 


the  constants  k  and  k'  were  called  the  coefficients  of  affinity 
of  the  direct  and  reverse  parts  of  the  complete  process  ;  as  we 
proceeded  it  was  found  possible  to  substitute  the  more  exact 
expression  reaction-velocity  for  the  vaguer  term  used  at  first. 
But  no  attempt  has  yet  been  made  to  analyse  these  coefficients, 
or  to  trace  connexions  between  their  values  and  the  composi- 
tion and  other  chemical  properties  of  the  bodies  which  take 
part  in  the  various  changes.  It  is  necessary  now  to  proceed 
to  this  part  of  our  subject. 

1  See  Ostwald,  Lehrbuch,  2.  728—740. 


CHAPTER    III. 


CHEMICAL  AFFINITY. 


209  IN  Chapter  I.  of  this  Book  I  have  placed  before  the 
student  a  sketch  of  the  views  concerning  chemical  affinity 
which  prevailed  before  the  publication  of  Berthollet's  Essai 
de  Statique  Chimique;  I  have  tried  to  shew  the  importance 
of  Berthollet's  assertion  that  every  chemical  change  is  con- 
ditioned not  only  by  the  affinities  but  also  by  the  masses 
of  the  interacting  bodies  ;  I  have  passed  in  review  the  work 
of  Guldberg  and  Waage,  which  led  to  an  accurate  statement 
of  the  law  of  mass-action,  by  incorporating  the  conception 
of  equivalency  with  that  of  mass,  and  by  considering  the 
distribution  of  the  members  of  a  changing  system  when 
equilibrium  is  established ;  I  have  given  a  short  account  of 
those  researches  by  Ostwald  and  others,  which,  while  con- 
firming the  ideas  of  Guldberg  and  Waage  by  applying  them 
to  different  classes  of  chemical  changes  and  rinding  the  ex- 
pression of  the  fundamental  law  appropriate  to  each  class, 
have  also  amplified  these  ideas  by  adding  to  the  law  of 
mass-action  the  principle  of  the  coexistence  of  reactions; 
I  have  tried  to  help  the  student  to  form  a  conception  of 
a  changing  chemical  system  as  swinging  in  two  directions 
until  equilibrium  is  attained,  and  to  regard  the  direct  and 
reverse  changes  as  conditioned  by  the  active  mass  and  the 
coefficient  of  affinity  of  each  member  of  the  system  ;  I  have 
sought  to  give  proofs  of  the  assertion  that  those  reactions 


408  CHEMICAL   AFFINITY.  [BOOK  II. 

which  seem  to  proceed  only  in  one  direction  are  really 
limiting  cases  of  equilibrium  ;  and  finally  I  have  glanced 
at  the  thermodynamical  and  the  molecular  methods  whereby 
the  law  of  mass-action  and  the  principle  of  the  coexistence  of 
reactions  have  met  with  a  general  confirmation.  . 
210  The  fundamental  equation  of  equilibrium,  kpq  —  k'p'q', 
assumes  a  more  workable  form  when  written 


In  these  equations  P,  Q,  P  ',  and  Q'  =  number  of  equivalents 
of  each  reacting  body  in  a  system  of  four  bodies  ;  p,  q,  /,  and 
q  =  active  mass  of  each  body  present  in  the  system  when 
equilibrium  is  established  ;  x  =  number  of  equivalents  of  P 
and  Q  decomposed,  and  number  of  equivalents  of  P'  and  Q' 
formed,  when  equilibrium  results  ;  and  k  and  k'  =  coefficients 
of  affinity  of  the  direct  and  reverse  change,  respectively. 
(v.  par.  169.) 

In  applying  this  equation  it  is  necessary  to  determine  x 
for  some  special  initial  values  of  P,  Q,  P',  and  Q',  hence  to 

find  the  value  of  the  ratio  y-,  to  use  this  value  in  order  to 

calculate  x  for  various  values  of  P,  Q,  P',  and  Q',  and  to 
compare  the  observed  values  of  x  with  those  thus  calculated. 
(For  examples,  v.  par.  170.) 

The  coefficients  k  and  k'  may  be  regarded  as  represent- 
ing the  chemical  forces  which  respectively  cause  the  formation 
of  P  and  Q',  and  the  re-formation  of  P  and  Q.  But  the 
notion  of  chemical  force  is  at  present  vague  and  inexact  : 
we  found  it  better  to  follow  van't  Hoff,  Guldberg  and  Waage, 
and  others,  in  regarding  k  and  k'  as  the  velocity-constants 
of  the  direct  and  reverse  change,  respectively.  As  thus  inter- 
preted, the  equation 


establishes  a  quantitative  connexion  between  the  equilibrium 
of  a  chemical  system  and  the  velocities  of  the  two  parts  into 
which  the  complete  change  may  be  divided. 


CH.  III.  §§  209—2 1  I  ]    AFFINITY-COEFFICIENTS.  409 

But  although  it  is  advantageous,  at  present,  to  regard  -p 

as  the  ratio  of  the  velocity-constants  of  the  two  parts  of  the 
complete  change,  yet  we  cannot  be  satisfied  with  this  inter- 
pretation. For  -r  represents  the  value  of  the  ratio  of  the 

affinity  of  the  two  bodies  P  and  Q  to  the  affinity  of  the  bodies 
P  and  Q'  produced  by  the  interaction  of  P  and  Q ;  and-  the 
elucidation  of  chemical  affinity  is  the  ultimate  object  of  our 
inquiry.  Let  us  then  examine  the  results  which  have  been 
obtained  by  applying  the  equation  of  equilibrium. 


SECTION  I. 

Specific  affinity  -coefficients  of  acids  and  bases. 

Ill  In  par.  181  the  application  of  the  equation  of  equilibrium 
to  a  system  of  four  bodies  was  considered.  The  bodies  A 
and  B  are  changed  to  A'  and  B'  ;  the  active  masses  of  the 
four  bodies  at  the  beginning  of  the  process  are  P,  Q,  P',  Q', 
respectively;  x  represents  the  number  of  equivalents  of  .A 
and  B  changed  to  A'  and  B  at  any  moment,  and  x  represents 
the  number  of  equivalents  of  A  and  B'  changed  to  A  and  B 
at  the  same  moment  ;  c  is  the  velocity-constant  of  the  direct 
change,  and  c  is  the  velocity-constant  of  the  reverse  change  ; 
then  the  velocity  of  the  direct  change  is 

(/>-*)  (<2-*)*; 

the  velocity  of  the  reverse  change  is 

(P'-x-](Q-x}c; 
and  the  velocity  of  the  total  change  is 


When  equilibrium  results  the  velocity  of  the  total  change 
must  =  o  ;  if  then  £  =  value  attained  by  x  when  equilibrium 
results,  we  have  the  conditions  of  equilibrium  expressed  in 
terms  of  the  velocities  of  the  two  parts  of  the  total  change  by 
the  equation 


4IO  CHEMICAL  AFFINITY.  [BOOK  II. 

If  the  initial  conditions  are  made  such  that  one  equivalent 
of  A  and  one  of  B  are  present  and  A'  and  B'  are  absent,  we 
have  P  =  Q  =  i,  and  F  =  Q  =  o  ;  the  equation  then  becomes 


and  hence 


As  £  can  be  determined  by  experiment,  the  ratio  of  the 
velocity-constants,  -,  ,  can  be  calculated. 

212  This  form  of  the  equation  of  equilibrium  has  been  applied 
by  Thomsen  to  the  case  of  the  interaction  between  an  acid 
and  the  neutral  salt  of  another  acid  in  dilute  aqueous  solution. 
When  equivalent  masses  of  hydrochloric  acid  and  sodium 
sulphate  interact,  Thomsen  found  that  f  =  f  ;  the  same  value 
was  found  when  nitric  acid  was  substituted  for  hydrochloric  ; 
these  results  were  on  the  whole  confirmed  by  Ostwald,  who 
employed  a  different  experimental  method.  (For  details,  v. 
pars.  183,  184.) 

By  repeated  experiments  with  a  neutral  salt  and  different 
acids  it  is  obvious  that  values  can  be  found  for  £  in  each  case  ; 
and  from  these,  values  are  at  once  deduced  for  the  ratio  of 

the  velocity-constants,  -;  .  This  ratio,  -j  .  is  the  same  as  the 

c  '  c  " 

/     fc    \2 

ratio  f    _    J  ,  so  that  to  express  the  ratio  in  question  we 

may   employ   either    form,   -,  or  (    £    J  ;    the  ratio  —  ~-  -..  is 

identical  with  that  formerly  expressed  by  the  symbols  j-,  ,  and 

called  the  ratio  of  the  affinities  of  the  reacting  bodies.  Hence 
investigations  conducted  on  the  lines  just  indicated  will  lead 
to  measurements  of  the  relative  affinities  of  different  acids  for 
the  same  base.  Such  investigations  have  been  conducted  by 
Thomsen,  Ostwald,  and  others. 

Suppose  that  equivalent  masses  of  Na2SO4  and  HC1  inter- 
act in  dilute  aqueous  solution  ;  the  direct  change  which  occurs 
will  result  in  production  of  NaCl  and  H2SO4,  but  these  will 


CH.  III.  §§2 1  I,  212]    AFFINITY-COEFFICIENTS.  4!! 

react  to  reproduce  Na2SO4  and  HC1 ;  if  measurements  of  £ 
are  made — i.e.  if  the  number  of  equivalents  of  each  body 
present  when  equilibrium  is  attained  is  determined — we  have 

values  for  the  ratio          „  which  is  the  same  as  \/  -.  or  T,- 

I  —  £  V    c  K 

We  thus  determine  the  ratio  of  the  affinities  of  the  two  acids, 
sulphuric  and  hydrochloric,  towards  the  base  soda.  If  another 
series  of  measurements  of  f  is  made  when  equivalent  masses 
of  Na2SO4  and  HNO3  react  in  dilute  aqueous  solution,  we 
shall  determine  the  ratio  of  the  affinities  of  the  two  acids 
sulphuric  and  nitric  towards  the  base  soda.  We  can  thus 
obtain  a  series  of  ratios  k  :  k' ,  k  :  k",  k  :  k"',  &c.  which 
express  the  relative  affinities  of  various  acids  towards  a 
specified  base  in  terms  of  some  one  acid  chosen  as  a 
standard. 

There  is  another  way  of  looking  at  the  meaning  of  the 
ratio  we  are  considering.  When  an  acid  interacts  with  an 
equivalent  mass  of  the  neutral  salt  of  another  acid  until  equi- 
librium is  attained,  the  number  of  equivalents  of  the  salt 
remaining  unchanged  is  i  —  £  (giving  the  same  meaning  to  £ 
as  before),  and  the  number  of  equivalents  of  the  salt  decom- 
posed is  £ ;  but  as  each  equivalent  of  salt  decomposed  pro- 
duces one  equivalent  of  base  and  one  of  acid,  f  is  also  the 
number  of  equivalents  of  the  base  which  has  combined  with 
the  added  acid,  and  I  -  £  expresses  the  number  of  equi- 
valents of  the  base  which  has  remained  in  combination  with 

the  first  acid.     The  ratio      ,,     then  expresses  the  distribution 

of  the  base  between  the  acids.  Thus  in  the  case  of  Na2SO4 
reacting  with  H2N2O6,  Thomsen  found  £  =  f ;  that  is,  f  of  the 
base  (Na2O)  had  entered  into  combination  with  nitric  acid, 
and  ^  of  the  base  remained  combined  with  sulphuric  acid, 
when  equilibrium  was  attained.  Hence,  if  the  affinity  of  an 
acid  is  measured  by  the  quantity  of  a  base  with  which  it  com- 
bines when  competing  for  the  base  with  another  acid  in  dilute 
aqueous  solution,  the  three  compounds  being  present  in  equi- 
valent quantities,  it  follows  that  the  affinity  of  nitric  acid  for 
soda  is  twice  that  of  sulphuric  acid  for  the  same  base. 


412  CHEMICAL   AFFINITY.  [BOOK  II. 

Thomsen  uses  the  term  avidity  of  an  acid  for  a  base,  but 
it  seems  better  not  to  introduce  a  new  term  when  we  have 
already  employed  the  word  affinity  to  express  the  same  con- 
ception. 

The  following  numbers  are  taken  from  Thomsen's  Unter- 
suchungen  (i.  308) : 

Relative  affinity. 

Nitric  acid  ro 

Hydrochloric  acid  i'o 

Hydrobromic  acid  0*89 

Sulphuric  acid  0*49 

Dichloracetic  acid  0*36 

Oxalic  acid  0*24 

Monochloracetic  acid  0*09 

Acetic  acid  0*03 

Take  the  numbers  for  sulphuric  and  monochloracetic 
acids,  '49  and  '09 ;  these  numbers  tell  that  when  one  equi- 
valent of  sulphuric  acid  reacts  with  one  equivalent  of  sodium 
monochloracetate  in  dilute  solution  until  equilibrium  is  estab- 
lished, the  base  divides  itself  between  the  acids  in  the  ratio 

I  —  £      '40 
•49  :  "09;   or       ..     =  ~  ;    hence   £='155;    in    other   words, 

15*5  p.  c.  of  the  total  soda  remains  combined  with  the 
monochloracetic  acid  and  84^5  p.  c.  enters  into  combination 
with  the  sulphuric  acid. 

113  The  thermal  methods  employed  by  Thomsen,  and  the 
volumetric  methods  used  by  Ostwald,  for  determining  the 
distribution  of  a  base  between  two  acids,  when  the  three 
bodies  react  in  equivalent  quantities  in  dilute  solutions,  have 
already  been  described  (pars.  183,  184).  Ostwald  conducted 
a  series  of  experiments  with  the  special  purpose  of  determin- 
ing whether  the  relative  affinity  of  an  acid  varies  with  varia- 
tions in  the  base1.  The  acids  compared  were  nitric  and  sul- 
phuric, hydrochloric  and  sulphuric,  and  hydrochloric  and 
nitric ;  the  bases  were  potash,  soda,  ammonia,  magnesia,  zinc 
oxide,  and  cupric  oxide.  The  following  table  shews  the  ratio 
in  which  an  equivalent  of  each  base  divided  itself  between  an 
equivalent  of  each  acid: — 

1  See  Lehrbuch,  2.  784;  or  J.ftir  prakt.  Cliemie,  (2).  16.  385. 


CH.  III.  §§  212,  213]    AFFINITY-COEFFICIENTS. 


413 


Rase. 


Potash 


Soda 


Ammonia 


Magnesia 


Zinc  oxide 


Copper  oxide 


RELATIVE  AFFINITIES. 

H2N206 
H2SO4  ' 

^=2-00 
o-333 


0-333 
0-652 


0-638 

0-617 
?383 


=  r6i 


0-409 


0-97 


The  ratio  of  the  affinities  of  hydrochloric  and  nitric  acids 
is  evidently  independent  of  the  nature  of  the  base,  whereas  in 
the  case  of  sulphuric  and  hydrochloric,  or  sulphuric  and 
nitric,  acids,  the  ratio  varies  in  accordance  with  the  nature  of 
the  base.  The  reason  for  this  apparent  difference  is  to  be 
sought  for  in  the  numbers  which  express  the  volume-changes 
attending  the  action  of  sulphuric  acid  on  normal  sulphates. 
Ostwald  shews  that  when  sulphuric  acid  and  normal  sulphates 
react  in  equivalent  quantities,  only  a  portion  of  the  sulphate 
is  changed  into  the  acid  salt,  and  that  the  amount  of  this 
change  depends  on  the  base  present  in  the  normal  sulphate. 
Hence,  Ostwald  concludes,  that 

"sulphuric  acid...  does  not  exert  affinity  on  a  base  with  its  whole 
mass  but  only  with  that  part  which  is  not  combined  to  form  acid 
sulphate.  The  greater  this  part,  the  greater  will  the  affinity  of  sulphuric 
acid  appear  to  be." 

It  is  probable  that  the  true  relative  affinity  of  sulphuric  acid, 
like  that  of  hydrochloric  and  nitric  acids,  is  independent  of 
the  nature  of  the  base  with  which  the  acid  combines. 

The  influence  of  temperature  on  the  relative  affinities  of 
the  three  pairs  of  acids  is  then  examined  by  Ostwald  in  the 
same  way  as  has  been  employed  for  examining  the  influence 
of  the  nature  of  the  base. 


4H  CHEMICAL  AFFINITY.  [ROOK  II. 

The  results  are  contained  in  the  following  table. 

RELATIVE  AFFINITIES  (for  Soda). 
Temp. 


H2N2O6 

H2C12 

H  Cl 

H2S04  ' 

'     H2S04" 

IIL     H^07 

^55=i-90 

0*659 

1^=1-02 

0-345 

0-341        93 

1-90 

0-667 

—  -  =  2'OO 

0-333 

0*657 
—  —  =1-92 
0*343 

1-92           , 
^-=0-96 

2'00          V 

0-669 

0-666 

I<99      0-Q8 

o-33i     -0" 

o-334     '" 

2-02          9 

40 

w  JJ1 

0-703  0-703 

60°          -J— 2-^- ->••*>, 


Here  again  the  relative  affinities  of  hydrochloric  and  nitric 
acids  remain  constant,  while  that  of  sulphuric  acid  varies  with 
variations  of  temperature.  The  variation  in  the  value  of  the 
relative  affinity  of  sulphuric  acid  is  shewn  to  be  inversely  as 
the  amount  of  acid  which  has  combined  with  the  normal 
sulphate;  this  confirms  the  provisional  conclusion  that  the 
true  relative  affinity  of  sulphuric  acid  is  in  all  respects 
comparable  with  the  relative  affinities  of  hydrochloric  and 
nitric  acids. 

The  final  result  of  these  experiments  is,  that  the  relative 
affinities  of  the  acids  are  expressed  by  constant  numbers. 

In  another  paper1,  Ostwald  extends  the  volumetric  method 
to  a  number  of  acids,  both  monobasic  and  dibasic,  including 
several  carbon-acids.  He  has  also  determined  the  refractive 
indices  of  many  of  the  solutions  of  acids,  bases,  and  salts, 
already  employed,  and  from  these  he  has  arrived  at  measure- 
ments of  the  amounts  of  change  ;  so  that  most  of  the  data  on 
which  his  calculations  are  based  have  been  gained  by  two 
independent  methods.  The  results  agree  very  well ;  Ostwald, 
however,  thinks  that  the  volumetric  method  gives  more  trust- 
worthy results  than  the  optical  method.  The  following  table 
presents  the  results  of  the  volumetric  experiments. 

1  J.fiirprakt.  Chemie,  (2).  18.  328;  Lehrbuch,  2.  785. 


CH.  III.  §§2  1  3,214.]    AFFINITY-COEFFICIENTS.  415 

PROPORTIONS  IN  WHICH  BASES  ARE  SHARED  AMONG  MONOBASIC 
ACIDS. 

ACIDS.  Potash.  Soda.  Ammonia.        Mean. 

1  Dichloracetic  :  nitric  77  77  75  76 

2  Dichloracetic  :  hydrochloric  74  75  73  74 

3  Dichloracetic  :  trichloracetic  70,73  71,71  70,72  71 

4  Dichloracetic  :  lactic  8  9  n  g 

5  Monochloracetic  :  trichloracetic        92  92  92  92 

6  Formic  :  trichloracetic  97  96  97  97 

7  Formic  :  lactic  43  46  48  46 

8  Formic  :  acetic  25  23  23  24 

9  Formic  :  butyric  21  21  19  20 

10  Formic  :  isobutyric  19  19  18  19 

11  Butyric  :  acetic  54  52  53  53 

12  Isobutyric  :  acetic  56  51  53  53 

13  Propionic  :  formic  78  80  79  79 

14  Glycollic  :  formic  43  44  45  44 

One  equivalent  of  the  neutral  salt  (of  potassium,  sodium, 
or  ammonium)  of  the  acid  placed  first  in  column  i  reacted 
with  one  equivalent  of  the  acid  placed  after  it  in  the  same 
column  ;  the  numbers  in  the  columns  of  bases  represent  the 
percentage  amounts  of  base  withdrawn  from  the  first  acid  by 
the  action  of  the  second. 

These  results  confirm  the  conclusion  that  the  relative 
affinities  of  the  acids  are  expressed  by  constant  numbers. 
214  This  question  of  the  constancy  of  the  numbers  expressing 
the  relative  affinities  of  acids  is  very  important.  Having 
shewn  by  experiment  that  the  question,  Are  these  numbers 
independent  of  the  nature  of  the  base?  must  be  answered  in 
the  affirmative,  Ostwald1  proceeds  to  examine  the  subject 
somewhat  as  follows. 

The  absolute  affinity  of  an  acid  A  for  a  base  B  is  a  func- 
tion of  both  ;  let  it  be  represented  by  f(A,  B};  then  by  putting 
A  and  A'  as  two  acids  and  B  and  B'  as  two  bases,  the  state- 
ment that  the  relative  affinities  of  the  acids  are  independent 
of  the  nature  of  the  bases,  may  be  put  in  the  form, 

f(A,B] 


f(A',B)    f(A',B'Y 

Lehrbwh,  2.  787;  J.  filr  prakt.  Chemic,  (2).  16.  442. 


416  CHEMICAL   AFFINITY.  [BOOK  II. 

And  by  changing  the  means  we  get 
f(A,  B)  _f(A',  B} 


But  the  second  equation  means  that  the  relative  affinities 
of  the  bases  are  independent  of  the  nature  of  the  acids. 
Hence  the  affinity  between  an  acid  and  a  base  is  the  product 
of  two  specific  affinity-coefficients,  one  of  which  belongs  to  the 
acid  and  the  other  to  the  base. 

This  conclusion  is  of  very  great  importance;  it  rests  on 
the  experimental  evidence  already  sketched,  but  it  is  also 
confirmed  by  a  large  amount  of  indirect  evidence.  An  exam- 
ination of  this  evidence  leads  us  not  only  to  place  greater 
trust  in  the  accuracy  of  the  conclusion  already  stated,  but  it 
also  shews  how  values  have  been  found  for  the  affinities  of 
many  acids  by  methods  other  than  the  thermal  method 
used  by  Thomsen  and  the  volumetric  method  employed  by 
Ostwald. 

215  When  acetamide  is  brought  into  contact  with  water 
and  an  acid,  it  is  changed  to  acetic  acid,  and  ammonia,  which 
combines  with  the  acid. 

The  change  may  be  formulated  thus, 

CH3.CO.NH2  +  HSO  =  CH3.CO.OH  +  NH3. 

The  rate  of  this  change  varies  with  the  nature  of  the  acid 
used. 

If  each  acid  possesses  a  specific  affinity-coefficient,  we 
might  expect  that  the  reaction  under  consideration  would  be 
quantitatively  conditioned  by  the  value  of  the  coefficient  for 
each  acid  used. 

Now  we  have  already  seen  that  the  ratio  of  the  affinities 

of  two  acids  may  be  expressed  in  the  form  —  ^,  and  that 
this  ratio  is  equal  to  the  square  root  of  the  ratio  of  the 
velocity-constants  of  the  reaction  —  -  -  =  L/-f  ;  hence  if  the 

velocities  of  the  change  of  acetamide  to  acetic  acid  and 
ammonia  are.  measured,  using  different  acids,  we  shall  be  able 


CH.  III.  §§214— 2 1 6]      AFFINITY   COEFFICIENTS.  417 

to  find  the  affinity-constants  of  the  acids ;  and  the  values 
thus  obtained  may  be  expected  to  be  the  same  as  those 
deduced  for  the  same  acids  by  the  thermal  or  volumetric 
study  of  the  reactions  which  occur  when  these  acids  react 
with  bases1. 

The  course  of  the  change  was  observed  by  decomposing 
the  ammonium  salt  formed  by  sodium  hypobromite,  and 
measuring  the  nitrogen  evolved.  The  reaction  is  not  free 
from  secondary  changes;  the  ammonium  salt  formed  causes 
the  velocity-constant  of  the  stronger  acids  to  be  greater,  and 
the  constant  for  weak  acids  to  be  smaller,  than  would  be  the 
case  were  the  ammonium  salt  not  formed.  The  time  was 
determined  in  each  case  at  which  one-half  of  the  total  aceta- 
mide  had  been  changed ;  the  reciprocals  of  these  times  are  the 
velocity-constants  ;  and  the  square-root  of  the  ratio  of  these  is 
the  ratio  of  the  affinities  of  the  acids.  The  occurrence  of  se- 
condary reactions  makes  the  numbers  obtained  rather  doubtful ; 
nevertheless  the  order  of  the  affinities  of  the  acids  examined  is 
the  same  as  the  order  of  the  affinities  determined  by  the  more 
accurate  volumetric  method,  and  in  the  cases  of  the  stronger 
acids  the  individual  numbers  agree  very  fairly,  Ostwald  also 
determined  the  velocity-constants  when  the  reaction  had  pro- 
ceeded for  a  short  time  only;  under  these  conditions  but  little 
ammonium  salt  was  formed,  and  the  secondary  changes  were 
eliminated  to  a  considerable  extent.  When  the  values  thus 
obtained  are  compared  with  those  formerly  arrived  at,  the 
influence  of  the  secondary  reaction  caused  by  the  ammonium 
salts  is  very  marked,  especially  with  the  weaker  acids2. 
J16  When  methylic  or  ethylic  acetate  in  aqueous  solu- 
tion is  kept  at  a  moderate  temperature  the  acetate  is  very 
slowly  changed  to  alcohol  and  acid,  but  if  an  acid  is  added 
the  change  proceeds  more  rapidly ; 

CHS .  COOCH3  +  H2O  =  CH3 .  COOH  +  CH3 .  OH. 

1  See  Ostwald,  J.  fur  prakt.  Chetnie,  (2).  28.  449;  or  Lehrbuch,  2.  798.  It 
has  already  been  shewn  (par.  1 76)  that  the  reactions  in  question  follow  the  law  of 
mass-action  and  the  principle  of  the  coexistence  of  reactions. 

-  The  numbers  are  given  in  the  table  on  p.  421. 

M.  C.  27 


41  8  CHEMICAL   AFFINITY.  [BOOK  II. 

This  reaction  has  been  used  by  Ostwald1  for  determining  the 
affinities  of  many  acids  ;  the  velocity  of  the  change  was 
measured  by  titrating  with  a  standardised  baryta  solution,  as 
the  change  proceeded  the  amount  of  acid  in  the  liquid 
increased. 

As  only  a  limited  quantity  of  one  body  is  undergoing 
change,  the  velocity-constant  of  the  reaction  should  be  found 
by  the  formula  deduced  for  such  cases  from  the  law  of  mass- 

T  A 

action2,  viz.  c  =  ^log-,  -  where  A  =  number  of  equivalents 

v          si  —  X 

of  methylic  acetate  originally  present,  and  x  —  number  of 
equivalents  changed  in  time  6.  The  velocity-constants  of 
about  30  acids  have  been  determined  by  Ostwald,  and  from 
these  the  affinity-constants  have  been  calculated  in  terms  of 
hydrochloric  acid  as  unity  ;  the  results  agree  very  fairly  well 
with  those  previously  obtained  ;  in  the  cases  of  weak  acids 
the  values  found  by  the  methyl  acetate  method  are  con- 
siderably larger  than  those  deduced  from  the  observations 
with  acetamide. 

217  The  inversion  of  cane-sugar  by  means  of  acids  in  dilute 
solution  has  been  used  by  Ostwald  as  a  third  process  whereby 
values  may  be  found  for  the  affinities  of  various  acids3; 


The  velocity  of  the  change  was  determined  by  measuring 
the  amount  of  inverted  sugar  by  means  of  Fehling's  solution. 
The  same  formula  was  employed  as  was  used  for  calculating 
the  velocity-constants  of  the  change  of  methylic  acetate  to 
alcohol  and  acid.  The  results  are  in  keeping  with  those 
formerly  obtained  ;  but  as  the  inversion-process  is  more  free 
from  secondary  reactions  than  either  the  acetamide-process  or 
the  methyl  acetate  process,  the  values  found  for  the  affinities 
of  the  acids  by  the  first-named  method  are  to  be  preferred  to 
those  obtained  by  the  other  methods. 


1  y.fur prakt.  Chemie,  (2).  28.  449;  or  Lehrlutch,  2.  803. 

2  See  par.  174. 

3  Lehrbuch,  2.  810. 


CH.  III.  §§2  1 6— 219]   AFFINITY   COEFFICIENTS.  419 

218  Some  other  reactions  in  which  acids  take  part  have  been 
examined  by  Ostvvald  with  the  view  of  determining  whether 
the  reactions  are  quantitatively  conditioned  by  the  affinities  of 
the  acids. 

Ammonia  solution  reacts  with  bromine  to  form  nitrogen 
and  hydrobromic  acid ;  if  an  acid  is  present,  an  ammonium 
salt  is  produced  and  the  change  proceeds  more  slowly. 
Ostwald1  has  shewn  that  the  stronger  acids  retard  this 
change  more  than  the  weaker  acids,  and  that  the  times  re- 
quired for  a  definite  amount  of  the  change  to  be  accomplished 
vary  approximately  inversely  as  the  affinities  of  the  acids. 

In  another  memoir*,  Ostwald  has  examined  various  cases 
of  oxidation  and  reduction  occurring  in  presence  of  free  acids 
and  has  shewn  that  these  are  retarded  to  an  amount  propor- 
tional to  the  affinities  of  the  acids.  The  reactions  examined 
were,  firstly,  that  occurring  between  bromic  and  hydriodic 
acids,  HBrO8Aq  +  6HIAq  =  HBrAq  +  3H8O  +  6IAq— the  re- 
tarding effects  of  about  a  dozen  acids  being  measured — and, 
secondly,  that  occurring  between  chromic  acid  and  iodine, 

2CrO3Aq  +  6HIAq  =  2CrO3H3  +  61  Aq. 

The  change  which  occurs  when  solid  calcium  oxalate  reacts 
with  various  acids  to  produce  a  soluble  calcium  salt  and  oxalic 
acid  has  also  been  examined  by  Ostwald3.  The  amount  of 
change  which  has  occurred  when  equilibrium  is  established 
depends  on  the  affinities  of  the  acids  employed*. 

219  A  few  determinations  have  been   made  of  the  velocity- 
constants   of    reactions    brought    about   by   bases.      Warder 
measured  the  velocity  of  the  saponification  of  ethylic  acetate 

1  Zeits.fiirphysikal.  Chemie,1.  124. 

2  Ibid.  2.  127  ;  see  also  Burchard,  Zeils.  fiir physikal.  Chemie,  2.  796. 
8  Lehrbuch,  2.  793. 

4  Other  processes  have  been  employed  for  determining  the  distribution  of  the 
members  of  a  system  when  equilibrium  results,  or  when  a  certain  amount  of 
change  has  been  accomplished;  among  the  more  important  of  these  are  the 
colorimetric  method,  e.g.  measurements  of  amount  of  FeCl3  changed  to  Fe(SCy)8 
by  reacting  with  KSCyAq  (Gladstone,  Phil.  Mag.  (4).  9.  535);  and  optical 
methods,  especially  that  founded  on  measurements  of  rotatory  power  (v.  especially 
Jellet,  Trans.  Royal  Irish  Acad.  25.  391). 

27—2 


42O  CHEMICAL  AFFINITY.  [BOOK  II. 

by  soda1.  Reicher  extended  the  method  to  potash,  lime,  and 
a  few  other  bases2.  Ostwald  has  applied  the  same  process  to 
ammonia,  substituted  ammonias,  and  substituted  ammoniums3. 
The  results  can  be  regarded  only  as  a  starting-point  for  further 
investigations.  But  we  shall  see  that  the  electrical  method  of 
observation  is  to  be  preferred  to  that  based  on  the  saponifica- 
tion  of  ethereal  salts. 

220  There  is  then  a  large  amount  of  evidence  in  favour 
of  the  statement  that  many  different  reactions  of  acids 
are  quantitatively  conditioned  by  certain  coefficients  which 
depend  only  on  the  constitution  of  the  acids,  and  the  de- 
gree of  dilution,  and  are  independent  of  the  nature  of  the 
chemical  reaction.  These  coefficients,  or  affinity-constants, 
can  be  determined  by  different  methods.  Of  the  methods 
which  we  have  considered,  the  most  trustworthy  are  (i)  that 
based  on  the  inversion  of  cane-sugar,  (2)  that  wherein  the 
change  of  methylic  acetate  into  alcohol  and  acid  is  measured, 
(3)  that  which  rests  on  determinations  of  the  change  of  aceta- 
mide  into  acetic  acid  and  ammonia,  (4)  that  which  determines 
the  division  of  a  base  between  two  acids  either  by  measuring 
the  thermal  change  or  the  volume-change  which  accompanies 
the  chemical  change. 

The  following  table  presents  the  numbers  deduced  by 
Ostwald  for  the  affinities  of  various  acids  by  the  different 
methods. 

1  Amer.  Chem.  Journal,  1882.     No.  5. 

2  Annalen,  228.  257. 

3  Lehrlmch,  2.  819. 


CH.  III.  §§219,  22O]      AFFINITY   COEFFICIENTS. 

RELATIVE  AFFINITIES  OF  ACIDS.    (OSTWALD.) 


421 


ACID 

I 

sugar 
inversion 

II 

methyl 
acetate 

in 

acetamide 

IV 
division  of 
base 
between 
two  acids 

Hydrochloric 

100 

IOO 

IOO 

98 

Hydrobromic 

I05'5 

99'I 

98 

Hydriodic 

98-I 

— 

— 

Nitric 

100 

957 

98 

IOO 

Chloric 

ior8 

97-2 

— 

Sulphuric 

73-2 

73%93 
1[io4-56] 

65-4 

66 

Methane  sulphonic 

— 

100-37 

— 

— 

Ethane  sulphonic 

100 

99-33 

— 

— 

Propane  sulphonic 

— 

98-98 

— 

— 

Isobutane  sulphonic 



98-53 

— 

—  . 

Pentane  sulphonic 

— 

97-82 

— 

— 

Hexane  sulphonic 

95-4 

9894 

— 

— 

Isethionic 

95  '9 

98-87 

— 

— 

Benzene  sulphonic 

IO2'2 

99-54 

— 

— 

Formic 

12-4 

11-49 

5 

3'9 

Acetic 

6-32 

5-87 

2  '34 

1-23 

Propionic 

5-5i 

1-04 

Butyric 

— 

5'47 

— 

0-98 

Isobutyric 

579 

5-18 

— 

0*92 

Monochloracetic 

22 

20'8 

!3 

7 

Dichloracetic 

52-1 

48 

40-8 

33 

Trichloracetic 

86-8 

82-6 

80 

80 

Glycollic 

1  1'4 

— 

— 

— 

Diglycollic 

16-3 

— 

— 

— 

Lactic 

10-3 

9-49 

5 

3'3 

Methoxyacetic 

13-5 

Ethoxyacetic 

117 

— 

— 

— 

Methoxypropionic 

11-8 

— 

— 

— 

Hydroxyisobutyric 

10-3 

9-60 

— 

— 

Trichlorolactic 

26-3 

— 

— 

Pyruvic 

25-5 

25-9 

— 

— 

Oxalic 

43 

43 

22-6 

— 

Malonic 

17-5 

16*9 

— 

— 

Glyceric 

13-1 

— 

— 

— 

Succinic 

7-38 

7-04 

2'5 

i  "45 

Malic 

11  '3 

10-86 

4'7 

2-82 

Tartaric 

15-15 

7'5 

5  '2 

Pyrotartaric 

10-3 

Racemic 

15-15 

— 

— 

Citric 

13-1 

1279 

4 

— 

Phosphoric 

24-9 

— 

Arsenic 

21-9 

— 

— 

— 

1  The  affinity  of  sulphuric  acid  appears  less  than  that  of  its  derivatives  obtained 
by  replacing  hydrogen  by  indifferent,  or  even  basic,  radicles.  But  it  is  to  be  noted 
that  £  H2SO4  is  compared  with  SO2 .  OH  .  OCH8  &c.  If  molecular  quantities  are 
to  be  compared,  the  observed  numbers  for  sulphuric  acid  reactions  must  be 
doubled;  if  this  is  done  the  affinity  of  sulphuric  acid  is  104-56. 


422  CHEMICAL   AFFINITY.  [BOOK  II. 

None  of  these  numbers  can  be  accepted  as  final.  Some  of 
the  reactions  used  for  finding  the  affinity-constants  are  more 
free  from  secondary  changes  than  others.  It  has  already 
been  pointed  out  that  the  presence  of  normal  salts  tends  to 
make  the  stronger  acids  appear  stronger,  and  the  weaker 
acids  appear  weaker,  than  they  really  are.  This  influence 
exerted  by  normal  salts  also  depends  on  the  dilution  of  the 
acids  and  on  the  temperature;  the  subject  has  been  examined 
experimentally  in  a  series  of  memoirs  by  Spohr1.  The  ex- 
planation which  Spohr  gives  of  the  phenomena  is  based  on 
the  molecular  conception  of  chemical  action  which  was  shortly 
discussed  in  par.  193. 

221  Besides  the  methods  described  in  the  preceding  para- 
graphs, there  is  another  method  for  determining  the  relative 
affinities  of  acids  and  bases,  which  is  more  widely  applicable, 
more  easily  applied,  and  more  accurate,  than  any.  This 
method  rests  on  the  connexion  which  exists  between  the 
affinities  of  acids  and  the  electrical  conductivities  of  their 
aqueous  solutions. 

The  following  numbers2  shew  the  existence  of  a  definite 
connexion  between  the  electrical  conductivities  of  various 
acids  in  aqueous  solutions  and  the  velocity-constants  of 
chemical  reactions  conditioned  by  the  same  acids ;  the 
numbers  are  all  referred  to  hydrochloric  acid  =  100. 

1  J-  fur  prakt.  Chemie,  (2).  32.  32;  33.  265;  Zeitschr.  fur  physikal.  Chemie, 
2.  194  (especially  the  last  paper),    v.  also  par.  237. 

2  Ostwald,  Lehrbuch,  2.  823.     For  a  description  of  Ostwald's  methrds  and 
apparatus  for  measuring  the  conductivities  of  electrolytes  see  Zeils.  fiir  physikal, 
Chemie,  2.  561. 


CH. III. §§220,221]  ELECTRICAL  CONDUCTIVITIES  OF  ACIDS.  423 


ACID. 


Conductivities. 


Hydrochloric 

100 

Hydrobromic 

ion 

Nitric 

99-6 

Ethane  sulphonic 

79-9 

Isethionic 

77-8 

Benzene  sulphonic 

74-8 

Sulphuric 

65-1 

Formic 

1-68 

Acetic 

1-424 

Monochloracetic 

4'9 

Dichloracetic 

25-3 

Trichloracetic 

62-3 

Glycollic 

i-34 

Methyl  glycollic 

176 

Ethyl  glycollic 

1-30 

Diglycollic 

2-58 

Propionic 

0-325 

Lactic 

1-04 

Oxypropionic 

0-606 

Glyceric 

1-57 

Pyruvic 

5-60 

Butyric 

0-316 

Isobutyric 

0-311 

Oxyisobutyric 

1-24 

Oxalic 

197 

Malonic 

3'i 

Succinic 

0-581 

Malic 

i  '34 

Tartaric 

2-28 

Racemic 

2-63 

Pyrotartaric 

i  -08 

Citric 

1-66 

Phosphoric 

7-27 

Arsenic 

5-38 

Velocity-constants. 

Methylic  acetate    Inversion  of 
reaction.  sugar. 

100  100 

98  in 

92  100 


98 

99 
73'9 

0-345 

4'3 
23-0 
68-2 


0-304 
o'9 


6-70 
0-3 
0-268 
0*92 
17-6 
2-87 

1-18 
2-30 
2-30 

1-63 


92 
104 

i'53 
0-4 
4-84 
27-1 

75-4 
1-31 
1-82 
i-37 
2-67 

1-07 
0-8 
172 
6-49 

0-335 
i -06 
18-6 
3-08 

1-27 


1-07 
173 

6-21 

4-81 


The  agreement  between  the  values  in  the  three  columns 
for  these  acids  shews  that  there  is  a  close  parallelism  between 
the  electrical  conductivities  and  the  affinities  of  the  acids. 
The  three  sets  of  values  were  not  all  determined  for  equal 
dilutions  of  the  acids  used  ;  hence  the  first  question  to  be 
considered  in  inquiring  more  closely  into  the  connexion 


424  CHEMICAL   AFFINITY.  [BOOK  II. 

between  the  electrical  conductivities  and  the  affinities  of  acids 
is  ;  how  are  the  conductivities  modified  by  dilution  ? 

222  In  dealing  with  this  subject,  Ostwald  determines  the  mole- 
cular conductivities  of  the  acids  examined. 

Let  that  number  of  grams  of  an  acid  which  is  equal  to  the 
molecular  weight  of  the  acid  be  dissolved  in  water,  and  let  this 
solution  be  placed  in  a  vessel  the  parallel  sides  of  which  are 
formed  of  infinite  electrodes  placed  I  centim.  apart ;  then  the 
electrical  conductivity  of  this  system,  expressed  in  Ohms  or 
in  mercury  units,  is  defined  to  be  the  molecular  conductivity  of 
the  electrolyte.  The  molecular  conductivity  expresses  the 
quantity  of  electricity  which  is  conveyed  across  the  electro- 
lyte in  I  second  when  the  difference  of  potential  between  the 
electrodes  is  I  volt ;  inasmuch  as  each  ion  carries  the  same 
quantity  of  electricity  with  it,  the  quantity  carried  across  the 
electrolyte  measures  the  number  of  molecules  which  suffer 
electrolysis  in  the  process.  If  p  —  molecular  conductivity, 
and  X  =  electrical  conductivity  as  ordinarily  defined  (in 
mercury  units)  then  p,=  io7«X,  where  n  =  number  of  litres  to 
which  the  molecular  weight  of  the  acid  taken  in  grams  is 
diluted1. 

223  The  molecular  conductivities  of  solutions  of  acids  vary 
greatly  with  dilution.      This  statement  rests  on  the  expe- 
riments of  Arrhenius,  Kohlrausch,  and  others.     Considering 
first,  the  monobasic  acids,  Ostwald  has  arrived  at  the  law  of 
dilution  for  monobasic  acid*.     This  law  states  that  the  dilu- 
tions at  which  the  molecular  conductivities  of  monobasic  acids 
exhibit  equal  -values  bear  a  constant  relation  to  each  other.     For 
instance  the  molecular  conductivity  of  monochloracetic  acid 
at  any  dilution  is  equal  to  that  of  formic  acid  when  the  latter 
is  16  times  more  dilute  than  the  former,  and  is  equal  to  that 
of  butyric  acid  when  the  latter  is  256  times  more  dilute  than 
the  monochloracetic  acid. 

The  following  table  exhibits  some  of  the  data  on  which 
this  statement  rests.  Dilution  is  stated  in  litres ;  it  is  ex- 
pressed by  means  of  the  exponent  /,  which  is  defined  by  the 

1  Ostwald,  Lehrbuch,  2.  824. 

2  Lehrbuch,  2.  825—838;  or  Phil.  Mag.  Aug.  1886.  104. 


ON  r»  to  p  p  ; 


^,00  oo  o? 


ON  ON.OO    >H    w    M    .-H  qO 


to  O  N  fi  7^  yn  N 
4  tn  M  b  i^  c<  vb 

CO  -^-  "i\O  SO  t>.  tx 


•-    M    CO  ^  u^vO   t^OO 


1-1    H«    CS    CS    fO  -^  LO 


—  N  ro  Tf  un^O  t>-oo  OA  O 


.-*  *     P  r  ^P  P  ^  P 


HI    n    CO  rf  u-v\O   t^OO    ON  O 


^ntC'o  ^->« 


rj-  uvo   f>>OO   ON  O 


426  CHEMICAL   AFFINITY.  [BOOK  II. 

relation,  dilution  =  2P.  The  conductivities  are  here  expressed 
in  terms  of  an  arbitrary  unit  which  is  4-248  times  greater 
than  the  mercury  unit.  The  measurements  have  been  ex- 
tended to  nearly  100  monobasic  acids;  all -obey  the  law. 

The  conductivities  of  the  stronger  monobasic  acids  HC1, 
HBr,  HI,  HNOS,  HC1O8,  &c.  nearly  reach  their  maxima  in 
moderately  dilute  solutions;  hence  the  conductivities  of  these 
acids  vary  but  little  with  dilution.  The  conductivities  of  the 
weaker  monobasic  acids,  on  the  other  hand,  increase  largely 
as  dilution  increases ;  the  rate  of  this  increase  varies ;  the 
weaker  the  acid,  and  therefore  the  smaller  the  conductivity, 
the  greater,  as  a  rule,  is  the  increase  for  a  given  dilution. 
The  molecular  conductivities  of  the  stronger  monobasic  acids 
reach  a  maximum  equal  to  about  400  in  mercury  units,  at  a 
moderate  dilution;  the  conductivities  of  the  weaker  acids  also 
reach  a  maximum  in  very  dilute  solutions,  but  this  maximum 
is  not  quite  the  same  for  all  monobasic  acids1.  This  fact 
opens  a  new  inquiry;  if  there  is  a  close  parallelism  between 
the  chemical  reaction-velocities,  and  therefore  the  affinities,  of 
acids  and  the  electrical  conductivities  of  these  acids,  does  this 
parallelism  hold  between  the  affinities  and  the  maximum  con- 
ductivities, or  between  the  affinities  and  the  conductivities  at 
varying  dilutions  stated  with  reference  to  the  maximum  values? 
For  instance :  the  maximum  conductivities  of  hydrochloric, 
hydrobromic,  and  hydriodic,  acid  are  practically  identical, 
viz.  400  (in  mercury  units);  the  maximum  conductivities  of 
ethane  sulphonic  and  methane  sulphonic  acids  are  identical, 
viz.  368 ;  the  maximum  conductivities  of  isobutane  sul- 
phonic and  benzene  sulphonic  acids  are  identical,  viz.  356; 
moreover  the  rate  at  which  the  conductivities  increase  as 
dilution  increases,  stated  in  terms  of  the  maximum  conduc- 
tivities, is  practically  identical  in  these  three  groups  of  acids. 
Now  if  the  reaction-velocities  of  all  the  acids  in  any  one  of 
the  groups  are  the  same,  but  if  this  number  is  different  from 
the  value  for  any  other  of  the  three  groups,  we  must  conclude 
that  the  parallelism  between  conductivity  and  affinity  holds 

1  Ostwald,  Zeitschr.  fur physikal.  Chemie,  1.  74  and  97. 


CH.  III. §§223, 224]  ELECTRICAL  CONDUCTIVITIES  OF  ACIDS.  427 

good  between  maximum  conductivity  and  affinity;  on  the 
other  hand  if  the  reaction-velocities  of  all  the  acids  in  the 
different  groups  are  the  same,  we  must  conclude  that  the 
parallelism  holds  good  between  affinity  and  the  relative  con- 
ductivities at  varying  dilutions  stated  with  reference  to  the 
maximum  conductivities.  Should  it  appear  that  affinity  is 
closely  connected  with  maximum  conductivity,  it  will  only 
be  necessary  to  determine  the  conductivity  of  an  acid  in  a 
dilute  solution  in  order  to  find  its  affinity;  but  should  it  appear 
that  affinity  and  rate  of  increase  of  conductivity,  relatively 
to  maximum  conductivity,  are  closely  connected,  it  will  be 
necessary  to  determine  the  conductivity  of  an  acid  at  varying 
dilutions  until  the  maximum  conductivity  is  reached,  before 
an  approximate  value  is  found  for  its  affinity. 

The  following  numbers  shew  that  affinity  is  closely 
connected  with  relative  conductivity  and  not  only  with  maxi- 
mum conductivity1: — 


^ 


Reaction-velocity. 

ACID.  Methylic  acetate.  Sugar-inversion.  Conductivity. 

Hydrochloric  24-12  21*87                     4O1 

Hydrobromic  23-7  24-38                     403 

Hydriodic  23-33  401 

Methane  sulphonic  24-30  368 

Ethane  sulphonic  23-80  23-44                    367 

Isobutane  sulphonic  23-41  355                «, 

Benzene  sulphonic  23-94  22*82                    358 

The  acids  have  practically  identical  reaction- velocities ;  the 
rate  at  which  their  conductivities  increase  as  dilution  increases 
is  practically  the  same,  but  their  maximum  conductivities  are 
different. 

In  order  to  arrive  at  exact  determinations  of  the  affinities 
of  monobasic  acids  by  the  electrical  method,  it  is  therefore 
necessary  to  measure  the  conductivities  of  these  acids  in 
solutions  of  increasing  dilution  until  the  maximum  value  is 
obtained.  But  it  is  extremely  difficult  to  do  this  ;  indeed  the 
maximum  conductivity  of  a  weak  acid  cannot  be  directly 

1  Ostwald,  Zeitschr.  fur  physikal.  Chemie,  1.  78. 


428  CHEMICAL   AFFINITY.  [BOOK  II. 

determined,  because  at  great  dilutions  the  impurities  in  the 
water  affect  the  result  more  than  the  minute  trace  of  acid 
present. 

Ostwald1  has  examined  the  conductivities  of  weak  mono- 
basic acids  in  dilute  solutions.  The  starting-point  is  the 
generalisation  made  by  Kohlrausch2,  to  the  effect  that  the 
electrical  conductivity  of  a  salt  of  a  strong  monobasic  acid 
is  the  sum  of  two  constants,  one  of  which  depends  entirely  on 
the  nature  of  the  acid,  and  the  other  entirely  on  the  nature 
of  the  base.  Ostwald's  researches  shew  that  the  difference 
between  the  conductivity  of  a  strong  monobasic  acid  and 
that  of  its  sodium  salt  is  approximately  a  constant,  and 
that  this  value  becomes  more  nearly  constant  as  the  maxi- 
mum conductivity  is  more  nearly  approached.  Hence,  he 
concludes,  that  the  difference  in  question  has  a  constant  value 
when  maximum  conductivity  is  reached.  Similarly  the  dif- 
ference between  the  conductivity  of  a  strong  monobasic  acid 
and  its  potassium  salt  is  expressed  by  a  constant,  while 
another  constant  expresses  the  difference  when  a  lithium 
salt  is  used.  Further,  if  the  conductivities  of  solutions  of  a 
series  of  sodium  salts  of  strong  monobasic  acids  are  compared 
with  those  of  a  series  of  potassium  salts,  there  is  found  to  be 
a  constant  difference ;  e.g.  the  conductivity  of  the  lithium  salt 
is  always  approximately  97  units  less  than  that  of  the  sodium 
salt,  and  that  of  the  potassium  salt  is  always  approximately 
2i' i  units  less  than  that  of  the  sodium  salt.  The  conduc- 
tivity of  an  alkali  salt  of  a  strong  monobasic  acid  is  therefore 
the  sum  of  two  constants,  one  of  which  belongs  to  the  acid 
and  the  other  to  the  base ;  Kohlrausch's  generalisation  is  fully 
confirmed  for  the  alkali  salts  of  strong  monobasic  acids.  The 
constant  expressing  the  influence  of  the  base  may  be  found 
by  subtracting  the  maximum  conductivity  of  the  strong  acid 
from  that  of  its  normal  salt  with  the  base  in  question. 
>  In  a  more  recent  paper3,  Ostwald  develops  the  application 


1  Zeitschr.fur  physikal.  Chemie,  1.  78,  and  97. 

2  Wied.  Ann.  6.  167. 

3  Ostwald,  loc.  cit.  2.  840. 


CH.III. §§224,225]  ELECTRICAL  CONDUCTIVITIES  OF  ACIDS.  429 

of  the  law  of  Kohlrausch.  Kohlrausch's  law  may  be  put  in 
this  form ; 

p  =  k  (u  +  v) 

where  /j,  =  conductivity,  u  =  velocity  of  transference  of  one 
ion,  v  =  velocity  of  transference  of  the  other  ion,  and  k  — 
fraction  of  the  total  mass  of  electrolyte  that  is  dissociated  in 
the  solution  undergoing  electrolysis.  This  way  of  stating  the 
law  rests  partly  upon  the  hypothesis  which  Arrhenius  has 
developed  from  van't  Hoff's  law  of  osmotic  pressure,  viz.  that 
some  of  the  molecules  of  an  electrolyte  in  solution  are  disso- 
ciated into  their  ions,  and  that  the  greater  the  number  of 
dissociated  molecules  the  greater  is  the  conductivity  of  the 
electrolyte  (v. post,  par.  235).  Electrolytic  conductivity,  then, 
seems  to  depend  upon  (i)  the  amount  of  dissociation,  and  (2) 
the  velocities  of  motion  of  the  ions  into  which  the  molecules  of 
the  electrolyte  are  dissociated.  The  conductivity  of  a  binary 
electrolyte  at  infinite  dilution  may  be  stated  as  p  =  u  +  v. 
Kohlrausch1  has  shewn  that  the  conductivities  of  solutions  of 
sodium  chloride,  potassium  iodide,  and  similar  salts,  prac- 
tically reach  their  limiting  values  at  a  dilution  of  about  5000 
litres;  knowing  then  the  maximum  conductivity  of  one  of 
these  salts  in  solution,  the  velocity  of  transference  of  each  ion 
can  be  found,  provided  we  know  the  ratio  of  the  velocities  of 
the  two  ions  (for  the  maximum  conductivity  is  equal  to  the 
sum  of  the  two  velocities).  The  ratio  in  question  can  be 
determined  from  observations  of  the  variations  of  concentra- 
tion of  the  solution  during  electrolysis.  In  the  case  of  potas- 
sium chloride  the  mean  value  of  the  ratio  -  is  -94;  the  maxi- 
mum molecular  conductivity  of  the  salt  at  25°  is  140-3 
in  mercury  units2.  Hence  the  velocities  of  the  ions,  stated  in 
corresponding  values,  are 

K  =  67-9;  0  =  72-4. 
Similarly,  values  are  obtained  for  the  velocities  of  the  ions 


1    Wied.  Ann.  26.  198. 

-  Kohlrausch,  Pogg.  Ann.  103.  35. 


430  CHEMICAL   AFFINITY.  [BOOK  II. 

of  potassium  nitrate,  sodium  chloride,  and  sodium  nitrate; 
the  mean  values  are  as  follows:  — 


As  a  mean  value  for  the  velocity  of  hydrogen  as  an  ion, 
Ostwald  takes  the  number  320*5  at  25°;  this  value  may  require 
to  be  somewhat  altered. 

The  foregoing  treatment  of  the  law  of  Kohlrausch  furnishes 
Ostwald  with  a  means  for  finding  the  maximum  conductivity 
of  a  monobasic  acid.  Let  M=  maximum  conductivity  of  the 
acid;  let  /A  =  maximum  conductivity  of  the  sodium  salt  of  the 
acid;  then  /*  =  44'5  +  m,  where  m  is  the  velocity  of  transference 
of  the  negative  ion,  44*5  being  the  velocity  of  the  positive  ion, 
viz.  sodium.  Then  as  the  positive  ion  of  the  acid  is  hydrogen, 
and  as  the  velocity  of  this  ion  is  320*5,  we  have 

M=  320*5  +  m  ;  and  therefore  M  =  fj,  +  276. 

In  other  words;  to  find  the  maximum  conductivity  of  a 
monobasic  acid,  in  mercury  units  at  25°,  add  276  to  the 
maximum  conductivity  of  the  sodium  salt  of  the  acid. 

But  it  must  be  remembered  that  dilution  affects  the  con- 
ductivities of  the  normal  salts  of  weak  and  strong  mono- 
basic acids  in  the  same  way,  e.g.  dilution  from  32  to  1024 
litres  raises  the  conductivity  of  the  sodium  salts  of  all  mono- 
basic acids  about  10  units.  This  fact,  established  by  Ostwald1, 
gives  a  means  for  finding  the  maximum  conductivity  of  the 
sodium  salt  of  a  monobasic  acid  from  the  observed  conduc- 
tivity at  stated  dilution,  without  introducing  a  serious  error. 
It  is  only  necessary  to  add  a  certain  number  to  the  observed 
conductivity;  the  value  of  this  number  is  independent  of  the 
nature  of  the  acid.  The  following  table2  gives  the  data  for 
sodium  chloride:  — 

Maximum  conductivity  at  25°  (Kohlrausch}  =  119-9. 


V 

M 

d 

a 

•v 

M 

d 

a 

32 

1  07  '6 

12-3 

288-3 

250 

113-9 

6-0 

282-0 

64 

109-9 

IOO 

286-0 

512 

115-8 

4'i 

280-1 

128 

1  1  2X> 

7-9 

283-9 

1024 

II7-S 

2-4 

278-4 

oo 

119-9 

— 

276-0 

1  Zeitschr.fiirphysikal.  Chemie,  1.  97.  2  Ostwald,  Ibid.  2.  843. 


CH. III.§§225, 226]  ELECTRICAL  CONDUCTIVITIES  OF  ACIDS.  431 

In  this  table  v  =  dilution  in  litres,  JJL  =  conductivity  in  mer- 
cury units  at  25°,  d=  difference  between  observed  and  maxi- 
mum conductivity,  and  a  =  276  +  dy  in  other  words  a  =  number 
to  be  added  to  conductivity  of  sodium  salt  at  stated  dilution 
to  obtain  the  maximum  conductivity  of  the  acid. 

In  using  this  table  it  is  assumed  that  the  acid  is  mono- 
basic. This  assumption  can  be  tested  by  finding  whether  the 
increase  in  molecular  conductivity  is  approximately  10  units, 
when  dilution  is  increased  from  32  to  1024  litres;  if  the  acid 
is  //-basic,  the  increase  will  be  approximately  n .  10  units. 

The  results  embodied  in  the  preceding  table  may  be  used 
to  determine  the  velocity  of  transference  of  the  negative  ions 
of  monobasic  acids.  The  method  consists  in  determining  the 
conductivity  of  the  sodium  salt  of  the  given  acid  for  a  stated 
dilution;  then  adding  the  number  required  to  give  the  maxi- 
mum conductivity  of  the  salt  (d  in  the  table);  and  finally 
deducting  44*5  (the  velocity  of  sodium  as  an  ion)  from  the 
result.  The  following  table  gives  Ostwald's  results  in  more 
convenient  form:  v  =  dilution  in  litres,  and  b  =  numbers  to  be 
deducted  from  molecular  conductivity  of  sodium  salt  at  dilu- 
tion v,  in  order  to  get  the  velocity  of  transference  of  the 
negative  ion: — 


•v  b 

32  32-2 

64  34'5 

128  36-6 


v  b 

256  38-5 

512  40-4 

1024  42' i 


co  44-5 

226  The  research,  of  which  a  condensed  account  is  given 
in  the  preceding  paragraph,  furnishes  a  method  for  finding 
the  maximum  molecular  conductivity  of  a  monobasic  acid  from 
observations  of  the  conductivity  of  its  sodium  salt  at  stated 
dilutions.  The  further  development  of  the  method  of  Ostwald 
(loc.  «'/.)  makes  it  probable  that  the  maximum  conductivity 
of  some  acids  may  be  calculated  from  a  knowledge  of  their 
composition  alone.  Ostwald1  calculates  the  velocities  of  the 
negative  ions  of  44  monobasic  acids  of  very  different  com- 
position; from  the  results  so  obtained  he  draws  conclusions 

1  Loc.  at.  847. 


432  CHEMICAL  AFFINITY.  [BOOK  II. 

regarding  the  connexions  between  the  composition  and  the 
velocities  of  transference  of  these  ions.    These  conclusions  are: 

(1)  isomeric  ions  travel  with  equal,  or  almost  equal,  velocities; 

(2)  as  the  number  of  atoms  forming  the  negative  ions  increases 
the  velocity  of  transference  of  the   ions  decreases;  (3)  the 
substitution  of  one  atom  by  another  influences  the  velocity 
with  which  the  ion  travels,  e.g.  the  velocity  is  decreased  by 
substituting  chlorine,  or  hydroxyl,  for  hydrogen,  but  this  effect 
is  marked  only  in  the  comparatively  simple  ions;  (4)  when  the 
number  of  atoms  forming  the  negative  ions  is  more  than  about 
12,  the  velocities  of  these  ions  seem  to  depend  almost  entirely 
on  the  number,  and  not  at  all,  or  hardly  at  all,  on  the  nature, 
of  the  atoms.     If  the  number  of  atoms  in  various  negative 
ions  is  taken  as  abscissae,  and  the  velocity  of  transference  as 
ordinates,  an  asymptotic  curve  is  obtained  running  convex  to 
the  abscissae-axis,  from  which  the  velocity  of  ions  formed  of 
more  than  about  12  atoms  can  be  calculated,  from  the  com- 
position of  these  ions,  to  within  +  i  to  2  units,  without  any 
measurements  of  conductivity.     Hence  it  becomes  possible 
to  find  the  maximum  conductivity  of  a  monobasic  acid  the 
negative  ion  of  which  is  composed  of  not  less  than  about  12 
atoms,  from  the  composition  of  the  acid  alone. 

227  The  relations  between  the  electrical  conductivities  and 
the  dilution  of  polybasic  acids  differ  from  those  established  for 
the  monobasic  acids.  The  polybasic  acids  conduct  as  if  they 
were  first  of  all  separated  into  hydrogen  and  a  radicle  con- 
taining replaceable  hydrogen,  then,  as  dilution  increases,  into 
hydrogen  and  a  radicle  containing  less  replaceable  hydrogen, 
and  finally  into  hydrogen  and  the  acidic  radicle  containing  no 
replaceable  hydrogen1.  In  other  words:  a  dibasic  acid  con- 
ducts at  first  as  if  the  ions  were  H  and  HR,  but  on  further 
dilution  the  ions  become  Hz  and  R\  so  the  stages  which  can 
be  distinguished  in  the  conduction  of  a  solution  of  a  tribasic 
acid  as  dilution  increases  are  three,  the  ions  being  (i)  //and 
H,R,  (2)  Ht  and  HR,  and  (3)  H3  and  R. 

When  polybasic  acids  form  unstable  and  easily  decom- 

1  Ostwald,  Lehrbuch,  2.  831  et  set/.,  (or  Phil,  Mag.  August,  1886). 


CH.  III.§§  226,227]  ELECTRICAL  CONDUCTIVITIES  OF  ACIDS.  433 

posed  normal  salts,  e.g.  selenious  acid  or  phosphoric  acid,  the 
molecular  conductivities  of  these  acids  follow  nearly  the  same 
course,  as  dilution  increases,  as  the  monobasic  acids.  In  the 
following  table  the  molecular  conductivities  of  selenious  and 
monochloracetic  acids  are  placed  side  by  side ;  dilution  is 
stated  in  litres. 

Dil.       H2SeO3       CH2C1.CO2H  Dil.     H2SeO3    CH2C1.CO2H 

2  32-5  2T2  256  igi  l6l 

4  41-4  297  512  231  199 

8  53-5  40-5  1024  267  236 

6  70-3  54-6  2048  295  270 

32  92-3  73-4  4096  312 

64     120  97'4 

128   154       126 

The  relations  between  the  dilution  and  the  molecular  con- 
ductivities of  the  polybasic  acids  which  form  stable  normal 
salts  with  neutral  reaction  are  different  from  those  just  de- 
scribed. The  molecular  conductivities  of  the  stronger  dibasic 
acids  of  this  class  increase  until  a  value  is  reached  about  the 
same  as  that  for  the  stronger  monobasic  acids;  at  about  this 
point  the  second  replaceable  hydrogen  atom  appears  to  take 
part  in  the  conduction,  the  ions  are  now  probably  Hz  and  R 
and  conductivity  increases  as  dilution  increases,  until  it 
reaches  a  maximum.  The  following  numbers  give  the  mole- 
cular conductivities  of  oxalic  acid,  sulphuric  acid,  and 
methane  disulphonic  acid.  Dilution  is  stated  in  litres. 

Dil.  H2C204  H2S04            CH2(S03H)2. 

2  120  394  569 

4  152  410  622 

8  187  428  651 

1 6  224  456  674 

32  261  494  694 

64  293  541  7ii 

128  319  592  727 

256  339  640  740 

512  355  684  75i 

1024  371  7^9  756 

2048  391  74i  /6o 

4096  420  753  757 

M.  C.  28 


434  CHEMICAL  AFFINITY.  [BOOK  II. 

Oxalic  acid  reaches  the  maximum  of  the  strong  monobasic 
acids  at  about  the  dilution  of  512  litres,  sulphuric  acid  has 
reached  this  maximum  at  2  litres,  while  the  molecular  con- 
ductivity of  methane  sulphonic  acid,  which  is  a  very  strong 
acid,  is  much  greater  even  at  2  litres  than  the  maximum 
value  for  the  strong  monobasic  acids.  Of  the  three  acids  here 
considered,  the  weakest  is  oxalic,  and  the  strongest  is  methane 
sulphonic;  the  changes  in  the  conductivity  of  oxalic  acid  as 
dilution  increases  follows  a  course  somewhat  similar  to  that 
noticed  in  the  case  of  a  fairly  strong  monobasic  acid,  say 
dichloracetic  acid,  until  a  dilution  of  512  litres  or  so  is  reached, 
after  which  the  second  replaceable  atom  of  hydrogen  probably 
begins  to  be  separated  and  the  electrolysis  proceeds  according 
to  the  scheme  H2  +  R.  The  molecular  conductivities  of 
dichloracetic  acid  are  given  in  order  that  they  may  be  com- 
pared with  those  of  oxalic  acid : — 


Dil.     CHC12.CO2H        Dil.     CHC12.CO2H        Dil.     CHC12.CO2H 

2 

109 

32 

2S6 

512 

339 

4 

146 

64 

286 

1024 

342 

8 

i83 

128 

308 

2048 

343 

16 

222 

2S6 

324 

The  changes  in  the  molecular  conductivity  of  sulphuric 
acid  as  dilution  increases  cannot  be  compared  strictly  with 
the  changes  of  conductivity  of  a  monobasic  acid ;  some  of 
the  second  replaceable  hydrogen  atoms  are  probably  sepa- 
rated even  in  solutions  so  concentrated  as  4  litres,  and  con- 
ductivity continues  to  increase  until  a  maximum  is  reached 
which  is  approximately  double  that  of  the  stronger  mono- 
basic acids;  but  the  influence  of  either  replaceable  atom  of 
hydrogen  cannot  be  wholly  separated  from  the  influence  of 
the  other.  If  the  equivalent  conductivities  of  sulphuric  acid — 
obtained  by  dividing  the  molecular  conductivities  by  two, — 
are  compared  with  those  of  a  monobasic  acid  there  is  still 
a  marked  difference  in  the  relations  between  conductivity  and 
dilution  in  the  two  cases. 

Methane  sulphonic  acid  is  a  decidedly  stronger  acid  than 
sulphuric;  in  this  case  dilution  influences  the  equivalent  con- 
ductivity (i.e.  molecular  conductivity  divided  by  two)  in 


CH  .  III.  §§  227,228]  ELECTRICAL  CONDUCTIVITIES  OF  ACIDS.  43$ 

much  the  same  way  as  it  affects  the  conductivity  of  a  strong 
monobasic  acid.  The  numbers  for  nitric  acid  are  given,  and 
beside  them  are  placed  the  equivalent  conductivities  of 
methane  sulphonic  acid:  — 


3 

2 

3 

2 

J-Slt*  \ 

2 

2 

331 

285 

32 

367 

347 

512 

377 

376 

4 

342 

3" 

64 

371 

356 

1024 

378 

378 

8 

352 

326 

128 

375 

364 

2048 

375 

380 

i6 

36i 

337 

256 

376 

370 

4096 

— 

378 

The  behaviour  of  tribasic  acids  resembles  that  of  dibasic 
acids.  Phosphoric  acid,  for  instance,  resembles  dichloracetic 
acid;  dilution  increases  the  molecular  conductivity  from  131 
at  2  litres,  to  293  at  64  litres,  and  345  at  2048  litres.  The 
maximum  of  a  fairly  strong  monobasic  acid  is  reached 
but  not  surpassed;  the  third  atom  of  replaceable  hydrogen 
probably  takes  very  little  part  in  the  electrolysis.  Strong 
tribasic  acids  would  probably  reach  a  maximum  conductivity 
approximately  equal  to  three  times  the  maximum  of  the 
strong  monobasic  acids,  and  the  equivalent  conductivities  of 
these  acids  would  probably  be  very  similar  to  the  molecular 
conductivities,  which  in  this  case  are  also  the  equivalent  con- 
ductivities, of  the  strong  monobasic  acids.  But  very  few 
tribasic  acids  have  yet  been  examined.  (See  also  par.  232.) 

The  researches  of  Kohlrausch  and  Ostwald1  have  esta- 
blished a  connexion  between  the  molecular  conductivities 
of  bases  and  the  dilution  of  solutions  of  these  bases  similar  to 
that  which  exists  between  the  conductivities  and  the  dilution 
of  acids. 

228  The  molecular  conductivities  of  the  strong  bases,  soda, 
potash,  lithia,  and  thallia,  increase  as  dilution  increases  in 
much  the  same  way  as  the  conductivities  of  the  strong  mono- 
basic acids  increase  ;  the  maxima  for  the  bases  seem  to  be 
about  |  of  those  for  the  acids. 

The  following  numbers8  shew  that  there  is  a  close  paral- 

1  See  Ostwald's  Lehrbuck,  2.  839  and  886. 
3  Ostwald,  Lehrbuch,  2.  839. 

28—2 


436  CHEMICAL  AFFINITY.  [BOOK  II. 

lelism  between  the  electrical  conductivities  and  the  reaction- 
velocities  of  bases  ;  the  reaction-velocities  were  determined  by 
observing  the  rate  of  saponification  of  ethylic  acetate  by  the 
different  bases;  the  numbers  are  stated  in  empirical  units  for 
convenience  sake. 


Saponification- 

Electrical 

BASE. 

velocities. 

conductivities. 

Soda 

162 

161 

Potash 

161 

149 

Lithia 

165 

142 

Thallia 

158 

156 

Ammonia 

'3 

4-8 

Methylamine 

19 

2O'2 

Ethylamine 

19 

20-5 

Propylamine 

18-6 

1  8'4 

Isobutylamine 

14-4 

I5-2 

Amylamine 

18-5 

1  8'6 

Allylamine 

4 

6-9 

Dimethylamine 

22 

23-5 

Diethylamine 

26 

28-3 

Trimethylamine 

7'3 

97 

Triethylamine 

22 

20'2 

Piperidine 

27 

2? 

Tetra-ethylammonium 

131 

128 

229  It  has  been  shewn  in  pars.  223  and  224  that  the 
affinities  of  acids  are  closely  connected  with  the  relative 
conductivities  of  these  acids  stated  in  terms  of  their  maxi- 
mum conductivities ;  and  that  it  is  necessary  to  determine 
the  conductivities  of  acids  at  varying  dilutions,  until  the 
maximum  is  reached,  in  order  to  arrive  at  exact  measure- 
ments of  the  affinities  of  these  acids  by  the  electrical  method. 
Pars.  224  and  225  contain  an  account  of  Ostwald's  method 
for  finding  the  relative  and  maximum  conductivities  of  mono- 
basic acids. 

Let  us  now  see  how  the  results  thus  obtained  are  applied 
to  find  the  affinities  of  the  monobasic  acids.  Ostwald's 
treatment  of  this  subject1  is  based  on  the  extension  by 
Arrhenius  to  electrolytic  phenomena  of  van't  HofFs  law  of 

1  Zeitschr.  fur  physikal.  Chemie,  2.  270. 


CII.III.§§228,229]  ELECTRICAL  CONDUCTIVITIES  OF  ACIDS.  437 

osmotic  pressure  (v. post  pars.  235,  237).  The  hypothesis  of 
Arrhenius  states  that  the  molecular  conductivity  of  an  electro- 
lyte in  solution  depends  on  the  number  of  molecules  of  the 
electrolyte  which  are  dissociated  into  their  ions,  and  on  the 
velocity  of  transference  of  these  ions.  The  differences  be- 
tween the  conductivities  of  different  acids  depend,  on  this 
hypothesis,  chiefly  on  differences  in  the  degrees  of  dissocia- 
tion of  the  molecules  of  these  acids.  At  infinite  dilution, 
all  the  molecules  of  the  electrolyte  are  supposed  to  be  dis- 
sociated into  their  ions. 

As  the  hypothesis  rests  on  the  identity  of  the  laws  ex- 
pressing gaseous  dissociation  and  dissociation  in  solution,  it 
follows  that  deductions  may  be  drawn  from  gaseous  dissocia- 
tion-phenomena and  applied  to  dissociations  in  solution.  Now 
if  a  gaseous  body  is  dissociated  into  two  gases,  temperature 
being  constant,  the  pressure  of  the  undissociated  portion,  /, 
bears  a  constant  relation  to  the  square  of  the  pressure  of  the  dis- 
sociated portion,  /,,  so  that  —,  =  c.  At  a  stated  temperature, 

the  pressure  of  a  gas  is  proportional  to  its  mass,  #,  and  in- 
versely proportional  to  the  volume,  v.  But  van't  Hoff's  law 
of  osmotic  pressure  states  that  the  osmotic  pressure  of  an 
undissociated  compound  in  solution  is  equal  to  the  pressure 
which  the  same  mass  of  that  substance  would  exert  did 
it  exist  as  a  gas  occupying  the  same  volume  as  is  occupied 
by  the  solution ;  hence  in  the  solution,  this  pressure,  /,  may 

be  put  as  proportional  to  -  ;  and   therefore   from   the  above 

*U 

uv       „ 
equation  — ^  =  C . 

Now  let  fjix  =  molecular  conductivity  of  a  binary  electro- 
lyte at  infinite  dilution,  and  let  /*„  =  molecular  conductivity 
of  volume  v  (i.e.  conductivity  of  v  litres  containing  one 
molecular  weight  in  grams  of  the  electrolyte)  ;  then  (by  the 

hypothesis)  the  fraction   -"-  expresses  the  portion  of  the  elec- 

A^oo 

trolyte  which  is  dissociated  in  terms  of  the  total  mass  of  the 
electrolyte  taken  as  unity.  Putting  this  fraction  as  «„ 


438  CHEMICAL   AFFINITY.  [BOOK  II. 

and  the   undissociated   portion  of  the  electrolyte  as  u,  we 
have 


Then    substituting  these  values  in   the  equation   —  ,  =  C,   we 

u\ 

have 


This  equation  may  be  put  in  the  more  convenient  form 
i  —m     _  „ 

where  m=—  ,  i.e.  the  molecular  conductivity  at  any  stated 
dilution  referred  to  the  maximum  molecular  conductivity. 

This  equation  states  that  ^—  v  must  have  the  same  value 

m* 

for  all  dilutions  of  any  one  binary  electrolyte. 

Ostwald  has  proved  that  the  value  of ^-  v  is  constant 

for  each  of  a  great  many  monobasic  acids1;  in  these  cases 
m  varied  from  "j  to  76,  and  the  value  of  C  varied  for  different 
acids  from  '129  to  15 '3. 

Now  the  affinity  of  an  acid  is  a  number  which  quanti- 
tatively conditions  the  chemical  reactions  of  the  acid,  and  this 
number  is  nearly  proportional  to  the  electrical  conductivity 
of  the  acid  in  aqueous  solution.  The  value  of  the  affinity- 
coefficient  of  an  acid,  according  to  the  hypothesis  of  van't 
Hoff  and  Arrhenius,  depends  chiefly  upon  the  degree  of  dis- 
sociation of  that  acid,  for  the  greater  the  amount  of  dissocia- 
tion into  hydrogen  and  a  negative  ion  the  more  readily  will 
these  ions  enter  into  chemical  reactions;  and  inasmuch  as 
the  amount  of  dissociation  is  independent  of  the  nature  of 

1  Ostwald  (loc.  cit.}  shews  how  the  application  of  corrections  for  the  changes 
in  molecular  volumes  and  in  viscosity  which  accompany  the  concentration  of 
solutions  of  binary  electrolytes,  brings  the  observed  values  of  C  yet  more  near  to 
absolute  constancy. 


CH.  III.  §§229,  230]    AFFINITY   AND   CONSTITUTION.  439 

the  reactions  brought  about  by  the  acid,  it  follows  that  the 
affinity  of  an  acid  is  independent  of  the  nature  of  the  re- 
actions in  which  the  acid  takes  part. 

The  constant  obtained  by  applying  the  equation 

i  -  m 

— —  v  =  C 
m 

to  a  monobasic  acid,  represents  then  the  affinity  of  the  acid 
in  question. 

SECTION  II.     Connexions  between  tJie  affinity -coefficients  and 
tJte  constitution  of  acids, 

230  Ostwald  has  shewn  that  the  affinity-coefficients  of  many 
monobasic  acids  are  very  nearly  proportional  to  their  mole- 
cular electrical  conductivities  in  solution  stated  as  fractions 
of  the  maximum  conductivities.  This  statement  asserts  that 
a  number  can  be  found  for  each  acid  which  measures  its 
readiness  to  conduct  electricity  in  solution,  and  also  its 
readiness  to  take  part  in  chemical  reactions,  and  that  this 
number  depends  only  on  the  nature  of  the  acid,  and  is  in- 
dependent of  the  degree  of  dilution.  Put  into  the  form  of 
an  equation  by  which  the  number  in  question  can  be  deter- 
mined, the  statement  is 

i  —  m  ~ 
— *—  v=C; 
m* 

where  m  =  —  ; 

Moo 

fj,v  being  the  conductivity  of  a  solution  of  one  molecular 
weight  in  grams  in  v  litres  of  water,  and  /i^  being  the  maxi- 
mum molecular  conductivity  at  infinite  dilution. 

In  applying  this  equation  to  the  measurement  of  affinities 
of  acids,  Ostwald1  prefers  to  put  it  in  the  following  form  : 


( i  —  in)  v 
where  &  =  -£>     The  reason  for  this  form  is,  that  C  has  small 

1  Konigl.  Sachsischen  Geselhchaft  der  Wissenschaften  (rnath.-physische  Classe), 
Bd.  26  [1889].     (Also  in  Zeitschr.fiirphysikal.  Chemie,  3.  170.) 


440  CHEMICAL  AFFINITY.  [BOOK  II. 

values  for  strong  acids  and  large  values  for  weak  acids.  To 
avoid  small  fractions,  Ostwald  multiplies  m  by  100,  and  also  k 
by  100;  he  gives  values  for  look  at  dilutions  varying  from  8 
to  1024  litres,  and  finally  he  expresses  the  most  probable 
value  for  look  as  K. 

231  Ostwald  has  determined  K  for  more  than  100  mono- 
basic acids.  The  following  are  selections  from  his  results  for 
various  series  of  acids. 


ACETIC  ACIDS,  CnH^  +  ^COOH  AND  THEIR  DERIVATIVES. 


ACID. 

K. 

Formic 

H.COOH 

•0214 

Acetic 

CH3.COOH 

•0018 

Propionic 

C2H5.COOH 

•00134 

Butyric 

C3H-.COOH 

•00149 

Isobutyric 

CH(CH3)2.COOH 

•00144 

Valeric 

C4H9.COOH 

•00161 

Caproic 

C6Hn.COOH 

•00145 

Monochloracetic 

CH2C1.COOH 

•155 

Dichloracetic 

CHCLj.COOH 

5'H 

Trichloracetic 

Cdg.COOH 

121* 

Monobromacetic 

CH2Br.COOH 

•138 

Cyanacetic 

CH2Cy.COOH 

'37 

Sulphocyanacetic 

CH2SCy.COOH 

•265 

I  sosulphocyanacetic  1 

C3H302SN 

•000024 

Carbaminthioglycollic2 

CH2(SCONH2).COOH 

'0246 

Thio-acetic 

CH3.COSH 

•0469 

Thioglycollic 

CH2SH.COOH 

•0225 

*  Approximate  only. 

OXYACETIC  ACIDS,  CnH2BOH .  COOH,  AND  THEIR  DERIVATIVES. 

ACID.  K. 

Glycollic  CH2OH.COOH  -0152 

Methoxy-acetic  CH2(OCH3).  COOH  -0335 

Ethoxy-acetic  CH2(OC2H6).  COOH  -0234 

Phenoxy-acetic  CH2(OC6H5).  COOH  -0756 

0-Nitrophenoxy-acetic  CH2(OC6H4.  NO2).  COOH  -158 

P-            »            »  »                       »  '153 

1  By  action  of  chloracetic  acid  on  sulphocarbamide  (Volhard,   J.  fur  prakt. 
Chemie,  1874.  6;  Claesson,  Ber.  10.  1352). 

2  Claesson,  Ber.  10.  1350. 


CH.  III.  §§230,  231]    AFFINITY   AND  CONSTITUTION.  441 

ACIDS  DERIVED  FROM   AMIDOACETIC,   CH2  .  NH2  .  COOH. 

ACID.  K. 

Amidophenyl-acettc          CH2  (C6H4N  H2) .  COO  H  -0039 

Hippuric  CH2(C6H5.  NH .  CO).  COOH  -0222 

Aceturic  CH2(NH .  C,H3O).  COOH  '023 

ACIDS   DERIVED   FROM   PROPIONIC,    CH3 .  CH,.  COOH. 

ACID.  K. 

Lactic  CH3.CHOH.COOH  -0138 

Oxypropionic  CH2OH .  CH2.  COOH  '00311 

'     Glyceric  CH2OH .  CHOH .  COOH  -0228 

Laevulic  CH2.  C2H3O.  CH2.  COOH  -00255 

lodopropionic  CH2I .  CH2 'COOH  '009 

Trichlorolactic  CC13 .  CHOH  .COOH  -465 

DERIVATIVES  OF  HIGHER  ACETIC  ACIDS. 
ACID.  K. 

Trichlorobutyric  C3H4C13.COOH         io'o 

Oxyisobutyric          (CH3)2.  CHOH .  COOH  -0106 

Nitrocaproic  C6H10.  NO,.  COOH  -0123 

Dinitrocaproic  CftH9.  (NO2)2.  COOH  -0694 

BENZOIC  ACID  AND  ITS  OXY-DERIVATIVES. 

ACID.  K. 

Benzole                                C6H5.COOH  '006 

i  :  2  Oxybenzoic                C8H4OH.COOH  -102 

I  :  3         »                                  »  '00867 

1:4,,                                 „  -00286 
Oxysalicylic 

COOH  :  OH  :  OH=i  12:3  -114 

Oxysalicylic  1:2:5  *IQ8 

„         1:2:4  -0515 

,,1:2:6  5-0 
Dioxybenzoic 

COOH  :  OH  :  OH  =  i  :  3  :  4  -0033 

Dioxybenzoic                   I  :  3    5  '0091 

HALOGEN  DERIVATIVES  OF  BENZOIC  ACID. 
ACID.  K. 

o-  Chlorobenzoic  C6H4C1.COOH         -132 

m-  „  „  'OI55 

P-  „  „  -0093 

0-Bromobenzoic  C6H4Br.COOH         '145 

'«-  „  »  'OI37 

w-Fluobenzoic  C6H4F.COOH         -0136 

w-Cyanobenzoic  C8H4 .  CN .  COOH         -0199 


442 


CHEMICAL   AFFINITY. 
NlTROBENZOIC   ACIDS. 


[BOOK  ii. 


ACID. 

o-  Nitrobenzoic 
m-  „ 

P- 


C6H4.N02.COOH 


K. 
•616 

•0345 
•0396 


AMIDOBENZOIC  ACIDS  AND  THEIR  DERIVATIVES. 

The  values  of  K  for  the  three  isomeric  amidobenzoic  acids 
vary ;  the  acids  are  all  very  weak ;  the  meta  acid  is  the 
strongest  of  the  three. 

ACID.  K. 

o-  Acetamidobenzoic      C6H4 .  NHC2H3O  .  COOH         '0236 
m-  „  „  '0085 


P- 


•00517 


ACID. 
o-  Acetoxybenzoic 


DERIVATIVES  OF  OXYBENZOIC  ACID. 
C6H4(OC2H30)COOH 


m-  „ 

o-  Methoxybenzoic 

P- 


K. 

•°333 

„  -00422 

„  -00986 

C6H4(OCHa)COOH  -00815 

n  '00302 


HOMOLOGUES  OF   BENZOIC  ACID. 


C6H4.CH3.COOH         -012 

•00514 


ACID. 
0-Toluic 


Phenylacetic       C6H5.  CH2.  COOH        -00556 


UNSATURATED  ACIDS. 


ACID. 

K. 

Acrylic 

C2H3.COOH 

•0056 

Crotonic 

C3H2.COOH 

•00204 

Isocrotonic 

J5 

•0036 

Tiglic 

C4H7.COOH 

•0009 

Angelic 

„ 

•00501 

Hydrosorbic 

C5H9.COOH 

•00241 

Sorbic 

C6Hr.COOH 

•00173 

Parasorbic 

C6Hr.COOH 

•00173 

Methylacrylic 

C5H9.COOH 

•ooin 

CH.  III.  §§23  I,  232]    AFFINITY   AND   CONSTITUTION.  443 

ClNNAMIC  ACID  AND   DERIVATIVES. 

ACID.  K. 

Cinnamic  CH  (C6H5) .  CH .  COOH  -00355 

a- Bromo-cinnamic          CH  (C6H5).  CBr.  COOH  1-44 

0-  „  CBr (C6Hfi).CH.  COOH  "093 

Phenylpropiolic  C6H5.C2.COOH  -59 

0-Nitrophenylpropiolic        C6H4NO2.  C2.  COOH  ro6 

DERIVATIVES  OF  THE  BENZENOID  SULPHONIC  ACIDS. 
The  benzenoid  sulphonic  acids  are  so  strong  that  their 
affinity-constants  cannot  accurately  be  determined  by  the 
electrical  method ;  at  moderate  dilutions  as  much  as  90  per 
cent,  of  an  acid  of  this  group  seems  to  be  dissociated.  When 
the  amido-group  (NH2)  is  introduced  in  place  of  hydrogen, 
the  affinity  of  a  sulphonic  acid  is  decreased,  and  measure- 
ments can  be  made  by  the  electrical  method. 

ACID.  K. 

o-  Amidobenzene  sulphonic  C6H4.  NH2.  SO3H  '33 

m-  „  „  '0185 

P-  »  „  -0581 

Diamidobenzene  sulphonic 

SO3H  :  NH2  :  NH,=  i  =  2:3  -005 
Bromamidobenzene  sulphonic 

SO3H  :  NH2  :  Br=i  12:5  1-67 

Bromamidobenzene  sulphonic  1:3:6  '072 

Dibromamidobenzene  sulphonic  1:2:4:5  7-9 

„  1:2:3:5  very  strong ; 

K  shews  irregularities. 

1:3:4:6  2-5 

Toluidine  sulphonic  SO3H  :  NH2  :  CH3=i  :  3  :  4  '0236 

»  »  1:4=2  -0357 

J  It  has  already  been  mentioned  (par.  227)  that  many 
dibasic  acids  conduct  as  if  they  were  separated  by  the 
current  into  hydrogen  and  a  negative  ion  HR,  and  on 
further  dilution  into  hydrogen  and  the  negative  radicle  R. 
Electrolysis  probably  takes  place  in  accordance  with  the 
two  schemes  (i)  H2R  =  H  +  HR,  (2)  HR=H+R;  both  of 
these  occur  more  or  less  together,  but  until  the  conductivity, 
and  hence,  by  hypothesis,  the  electrolytic  dissociation,  reaches 
about  half  its  maximum  value,  the  first  scheme  fairly  accu- 
rately represents  the  course  of  the  electrolysis.  Dissociation- 


444  CHEMICAL   AFFINITY.  [BOOK  IT. 

constants  can  be  determined  for  dibasic  acids  by  the  method 
already  described,  provided  only  those  values  of  the  con- 
ductivity are  used  for  which  m  is  less  than  -5.  If  the  con- 
ductivities are  greater  than  half  the  maximum  values  for 
monobasic  acids,  the  dissociation-constants  cannot  be  accu- 
rately determined  ;  yet  even  in  these  cases  comparison  of 
the  dilutions  at  which  the  relative  conductivities  of  the 
different  acids  are  equal,  or  nearly  equal,  gives  data  for  com- 
paring the  dissociation-constants  of  the  acids;  the  constants 
are  inversely  as  the  corresponding  dilutions '. 

Ostwald  has  determined  the  conductivities  of  many  di- 
basic acids,  and,  by  using  the  numbers  representing  relative 
conductivities  at  varying  dilutions  approximately  up  to  that 
dilution  whereat  the  second  phase  of  the  electrolysis  begins, 
he  has  found  values  for  K  which  enable  the  affinities  of  these 
acids  to  be  compared. 

The  following  numbers  are  selected  from  his  results. 

OXALIC  ACIDS  AND  DERIVATIVES. 

The  constant  for  oxalic  acid  itself  could  not  be  accurately 
determined  ;  even  at  a  dilution  of  32  litres,  the  acid  is  much 
more  than  half  dissociated.  From  his  observations,  Ostwald 
concludes  that  K  for  oxalic  acid  may  be  taken  in  round 
numbers  as  about  10. 


ACID. 

K. 

Malonic                               CH2(COOH)2 

•158 

Succinic                              C2H4(COOH)2 

•00665 

Glutaric                               C3H6(COOH)2 

•00475 

Adipic                                C4H8(COOH)2 

•00371 

Pimelic                              C5H10(COOH)2 

•00359 

Methylmalonic         CH  (CH3)  .  (COOH)2 

•087 

Ethylmalonic          CH  (C2H5)  .  (COOH)2 

•127 

Dimethylmalonic       C  (CH3)2  .  (COOH)2 

•077 

Methylsuccinic      C2H3  (CH3)  .  (COOH)2 

•0086 

Oxamic                           CONH2.COOH 

•80 

Oxaluric          CONH  (CONH2).  COOH 

4'5 

Oxanilic                CONH  (C6H5)  .  COOH 

I  '21 

o-  Chloroxanilic    CONH  (C6H4C1)  .  COOH 

2-03 

P- 

1'4 

Ostwald,  I.e. 


CH.  III.  §232]     AFFINITY   AND   CONSTITUTION.  445 

Malic  C2H3(OH).(COOH)2  '0395 

Inactive  malic  ,,  '0399 

Dextro-tartaric  C2H2(OH)2(COOH)2  -097 

Laevo-tartaric  „  '097 

Racemic  „  -097 

BENZENE  DICARBOXYLIC  ACIDS. 
ACID.  K. 

0-Phthalic  C6H4(COOH)2        -121 

m-        „  „  '0287 

Oxyterephthalic     C6H3(OH).  (COOH)2        -25      ' 
Nitrophthalic        C6H3(NO2).  (COOHU 
COOH  :  NO2  :  COOH  =  i  :  2  :  5} 

I  :  3  :  5         -60 

ACIDS   DERIVED   FROM    PYRIDINE1. 

ACID.  K. 

Picolinic  C5H4N.COOH  -0003 

Nicotinic  C5H4N.COOH  '00137 

Isonicotinic  „  -00109 

Lutidinic  C6H3N  (COOH)2(ay)  -60 

Cincomeronic  „          (/Sy)  '21 

Isocincomeronic  „          (a#)  -43 

Quinolinic  „  (a/3)  '30 

Pyridine  dicarboxylic  „          ($3')  "15 

a-  Methyl  pyridine  dicarboxylic        C6H2 .  CH3 .  N  (COOH)2  '20 

aa-  Dimethyl  pyridine  dicarboxylic    C5H  (CH3)2  N  (COOH)2  -34 

«y-  „  »  „  '55 

The  following  results  exhibit  the  influence  of  geometrical 
isomerism  (v.  pars.  93 — 95,  Book  I.).  The  formulae  are 
written  in  accordance  with  the  notation  of  Wislicenus. 

ACID.  K, 

H\_    ^/COOH 
Crotonic  TI   ^C — C\  „„  '00204 

^"3 


TT     -v 

Isocrotonic  _u  J>C— C\  ^  '0036  (approximate). 

L.ti3^ 

The  values  of  K  for  isocrotonic  acid  vary  from  '0028  to 

1  The  positions  of  the  carboxyl  groups  in  the  dicarboxyl  derivatives  of  pyridine 
are  indicated  by  the  scheme 

:M: 


446  CHEMICAL   AFFINITY.  [BOOK    II. 

'00347  ;  this  is  because  of  the  impossibility  of  completely 
separating  the  acid  from  admixed  crotonic  acid.  The  axially 
symmetric  isocrotonic  acid  is  certainly  stronger  than  the 
plane  symmetric  crotonic  acid. 

The  values  of  K  for  tiglic  and  angelic  acids,  C6H8O2,  are  ; 
tiglic  acid  ='000957,  angelic  acid  =  '00501.  It  is  therefore 
probable  that  angelic  acid  is  analogous  to  isocrotonic  acid, 
and  has  the  constitution 


r    r 
CH3^ 

while  tiglic  acid  is  probably 

CH3\ 

H/  \CH3 

In  the  cases  of  maleic  and  fumaric  acids,  C2H2(COOH)2, 
the  values  are;  maleic  acid  =  ri  7,  fumaric  acid  —'093.  In 
maleic  acid,  which  is  about  twelve  times  stronger  than  fumaric 
acid,  the  carboxyl  groups  are  probably  nearer  one  another 
than  in  fumaric  acid  ;  the  structure  is  indicated  by  the 
formulae 


^r     _ 
H^-  COOH  and  COOK/-  >H 

(maleic)  (fumaric) 

If  the  formulae  of  Wislicenus  for  citraconic  and  mesaconic 
acids  are  adopted,  viz. 

COOH       .        ,/-CH3 


VL^  \COOH  H-^     "\COOH- 

(citraconic)  (mesaconic) 

we  should  expect  citraconic  to  be  the  stronger  of  the  two 
acids.  The  values  obtained  for  K  are,  for  citraconic  '34, 
and  for  mesaconic  '079.  The  third  isomeride,  itaconic  acid  is 
very  weak;  ^  =  '012.  The  constitution  of  this  acid  is 
probably 

C°C°H!>C-C\COOH- 

233  The  results  obtained  by  Ostwald,  some  of  which  are 
recorded  in  the  preceding  paragraphs,  enable  conclusions  to 
be  drawn  regarding  connexions  between  the  constitutions 
and  the  affinities  of  acids.  In  the  acetic  series,  for  example, 


CH.  III.  §§232,233]    AFFINITY   AND   CONSTITUTION.  447 

affinity  decreases  from  formic  to  propionic  acid  and  then 
remains  nearly  constant  until  caproic  acid  is  reached.  The 
substitution  of  chlorine  for  hydrogen  in  an  acetic  acid  is 
attended  with  an  increase  of  affinity ;  the  value  of  K  is  in- 
creased to  a  smaller  extent  when  bromine  replaces  hydrogen  ; 
on  the  other  hand  the  group  CN  increases  the  affinity  more 
than  chlorine  does,  so  does  the  group  SCN,  but  SCN  is  less 
energetic  in  this  way  than  CN.  In  the  benzoic  acids,  substi- 
tution of  hydrogen  by  CN  increases  K  a  little  more,  but 
only  a  little  more,  than  is  effected  by  putting  chlorine  for 
hydrogen,  the  position  of  the  CN  group  in  one  case  being 
the  same  as  that  of  the  Cl  atom  in  the  other  case.  Substitu- 
tion of  sulphur  for  oxygen  in  the  group  COOH  in  acetic 
acid,  raises  K  from  '0018  to  '0469;  but  if  the  group  SH 
is  substituted  for  hydrogen  in  the  same  acid,  K  is  raised 
from  -0018  to  -0225  only. 

The  change  from  an  acetic  acid  to  the  corresponding 
oxyacid,  i.e.  the  substitution  of  OH  for  H,  raises  the  affinity, 
but  the  increase  is  much  less  than  when  Cl  is  put  in  place 
of  H.  The  group  OCHS  is  more  acidic  than  OH.  The 
acidic  character  of  the  group  OCtfH8  is  very  marked.  When 
OC6H4NO2  is  substituted  for  H,  in  an  acetic  acid,  the  increase 
of  K  is  approximately  equal  to  that  which  occurs  when  Cl 
is  substituted  for  H.  On  the  other  hand,  the  basic  character 
of  ammonia  derivatives  is  seen  by  comparing  K  for 

CH2(OC6H6)  COOH  [#  =  -0756], 
with  K  for     CH2  (C6H4NH8)  COOH  [K  =  -0039] : 

with  this  decrease  may  be  contrasted  the  increase  due  to 
putting  in  the  acidic  group  CO 

[K  for  CH2  (C6H8.  NH  .  CO)  COOH  =  -0222], 
or  the  acidic  group  C2H3O 

[K  for  CH2  (NH  .  C2H3O)  COOH  =  -023]. 

The  influence  of  the  relative  positions  of  the  different 
groups  is  apparent  when  we  compare  the  affinities  of  pro- 
pionic, oxypropionic,  lactic,  and  glyceric  acids  ; 


448  CHEMICAL  AFFINITY.  [BOOK  II. 

CH3.CH2.COOH  K=  -00134 

CH2OH.CH2.COOH  ^='00311 

CH3.CHOH.COOH  ^='0138 

CH2OH.CHOH.COOH  ^='0228 

The  influence  of  relative  position  is  well  shewn  in  the 
values  of  K  for  the  three  oxybenzoic  acids;  the  affinity  of 
the  ortho-acid  is  nearly  twelve  times  greater  than  that  of  the 
meta-acid,  and  the  affinity  of  the  meta-acid  is  about  three 
times  greater  than  that  of  the  para-acid.  Substitution  of  a 
second  OH  group  in  benzoic  acid  raises  the  affinity  a  little 
if  the  second  OH  group  is  placed  in  the  position  next  to 
the  first,  but  if  the  second  OH  group  is  placed  in  the  position 
next  to  the  COOH  group,  the  increase  in  the  value  of  K 
is  very  great ; 

C6H4.COOH.OH  1:2  K=   -102 

C6H3.COOH.OH.OH    1:2:3        K=  "114 
C6H3.COOH.OH.OH    1:2:6        K=$-o 

A  comparison  of  the  affinities  of  the  isomeric  chloro- 
and  bromo-benzoic  acids  shews  the  influence  of  the  arrange- 
ment of  the  substituting  groups  ;  the  nearer  the  acidic  groups 
are  placed  the  greater  is  the  affinity  of  the  acid.  Again 
the  effect  of  replacing  H  by  Cl,  and  by  NO2,  exhibits  at 
once  the  more  acidic  character  of  the  NO2  group,  and  also 
the  influence  of  position  : — 

Cl  substituted  for  H  in  C6H5.COOH  in  the  meta-position  raises 
K  from  '006  to  '0155. 

NO2  substituted  for  H  in  C6H8.COOH  in  the  meta-position  raises 
K  from  '006  to  '0345. 

Cl  substituted  for  H  in  C6H5.COOH  in  the  ortho-position  raises 
.AT  from  -006  to  '132. 

NO2  substituted  for  H  in  C6H6.COOH  in  the  ortho  position  raises 
K  from  -006  to  '616. 

The  effect  of  the  character  and  position  of  the  replacing 
groups  is  also  shewn  in  the  change  of  affinity  brought  about 
by  passing  from  benzoic  acid  to  ortho-  and  para-acetoxy- 
benzoic  acids,  and  from  benzoic  acid  to  ortho-  and  para- 
methoxy-benzoic  acids  ;  both  groups  raise  the  affinity  when 
they  are  placed  in  the  ortho-position,  and  both  lower  the 


CH.  III.  §233]          AFFINITY   AND   CONSTITUTION.  449 

affinity  when  they  are  placed  in  the  para-position;  the 
change  of  position  in  the  case  of  the  group  O  .  C2H8O  from 
ortho  to  para  decreases  the  affinity  to  about  ^  of  its  value, 
the  corresponding  change  of  position  in  the  case  of  the 
group  O  .  CHS  decreases  the  affinity  to  about  ^  of  its  value  : — 

O.C2H3O  substituted  for  H  in  C0H5.COOH  in  the  ortho-position 
raises  K  from  -006  to  '0333. 

O.CH-,  substituted  for  H  in  C6Hfi.COOH  in  the  ortho-position 
raises  K  from  '006  to  '00815. 

O .  C2H3O  substituted  for  H  in  C6H5 .  COOH  in  the  para-position 
lowers  K  from  '006  to  -00422. 

O  .  CH3  substituted  for  H  in  C6H5.COOH  in  the  para-position 
lowers  K  from  '006  to  '00302. 

That  the  affinity  of  an  acid  is  dependent  not  only  on  the 
character  of  the  radicles,  but  also  on  their  relative  positions, 
is  shewn  in  a  very  marked  way  by  comparing  the  values  of 
K  for  the  two  bromo-cinnamic  acids  : — 

CH(C6H5).CH.COOH        K=  '00355 
CH(C6H5).CBr.COOH        ^=1-44 
CBr(C6H5).CH.COOH        K=  '093 

Substitution  of  Br  for  H  in  one  case  increases  the  affinity 
about  400  times,  and  in  the  other  case  only  about  26  times. 

The  affinities  of  the  pyridine  dicarboxylic  acids  also  ex- 
hibit the  influence  of  position ;  what  one  may  perhaps  call 
the  strongest  position  for  the  COOH  group  is  that  nearest 
the  nitrogen  atom,  and  the  position  para  to  the  nitrogen  atom 
is  stronger  than  that  which  is  meta  to  the  nitrogen  atom. 

These  results,  regarded  as  a  whole,  point  to  a  close  con- 
nexion between  the  affinities  of  acids  and  the  space-arrange- 
ments of  the  atoms  which  form  the  molecules  of  the  acids. 
This  is  confirmed  by  the  measurements  of  the  affinities  of 
crotonic  and  isocrotonic,  maleic  and  fumaric,  and  citraconic, 
mesaconic,  and  itaconic,  acids1. 

1  For  further  data,  and  discussion  of  the  data,  Oswald's  memoir  must  be 
consulted. 


M.  C.  29 


45°  CHEMICAL   CHANGE.  [BOOK  II. 

SECTION  III.     Chemical  change. 

234        In  considering  Guldberg  and  Waage's  general  equation  of 
equilibrium 


the  quantities  k  and  ^'were  treated  as  the 'coefficients  of  affinity' 
of  the  direct  and  reverse  changes,  respectively;  in  a  later  con- 
sideration of  the  subject  k  and  k'  were  regarded  as  represent- 
ing the  velocity-coefficients  of  the  two  parts  of  the  complete 
change.  In  pars.  214 — 220  it  is  shewn  that  to  each  acid  may 
be  assigned  a  certain  number  which  is  the  affinity-coefficient 
of  that  acid,  and  that  the  value  of  this  coefficient  quantita- 
tively conditions  the  different  reactions  in  which  the  acid  takes 
part.  Pars.  221 — 229  are  devoted  to  a  sketch  of  the  electrical 
methods  whereby  values  are  obtained  for  the  affinities  of  the 
acids.  The  explanation  of  these  electrical  methods  rests  on 
a  development  of  the  molecular  dissociation-hypothesis  of 
Williamson  which  was  first  applied  to  electrolysis  by  Clausius 
(v.  par.  192). 

The  further  development  of  the  Clausian  hypothesis  is  due 
in  great  measure  to  the  labours  of  van't  Hoff,  Arrhenius,  and 
Ostwald.  An  account  has  been  given  in  the  preceding  sections 
of  this  chapter  of  the  results  of  some  of  Ostwald's  work  in  this 
direction,  and  reference  has  been  made,  from  time  to  time,  to 
the  'law  of  osmotic  pressure'  as  stated  by  van't  Hoff.  It  now 
remains  to  glance  at  the  investigations  whereby  this  law  has 
been  gained  and  at  the  extensions  of  the  law  to  explain  the 
phenomena  of  chemical  change  occurring  among  substances 
in  solution.  As  the  subject  is  not  yet  fully  elucidated,  and 
as  the  principles  involved  are  rather  physical  than  chemical, 
although  the  chemical  applications  are  of  paramount  import- 
ance, a  brief  account  of  the  fundamental  researches  will  suffice. 
235  In  1887  van't  Hoff  published  an  important  memoir1,  in 
which  he  sought  to  establish  similarities,  and,  under  certain 
conditions,  identities,  between  substances  in  dilute  solution 
and  in  the  gaseous  state.  If  an  aqueous  solution  of  a  sub- 

1  Zeitschr.  fur  physikal.  Chemie,  1.  481  (Translation  in  Phil.  Mag.,  August, 
1888). 


CH.  III.  §§234,235]        OSMOTIC   PRESSURE.  451 

stance  is  contained  in  a  vessel  the  walls  of  which  are  perme- 
able by  water  molecules  but  not  by  the  molecules  of  the 
dissolved  substance,  and  the  vessel  is  immersed  in  water, 
water  will  enter  the  vessel,  and  the  pressure  on  the  walls  will 
increase  until  equilibrium  results,  after  which  no  more  water 
will  enter.  The  pressure  on  the  walls  of  the  vessel  is  called 
osmotic  pressure.  If  the  vessel  had  been  furnished  with  a 
movable  piston,  the  same  condition  of  equilibrium  might  have 
been  obtained,  without  the  entry  of  water,  by  compressing  the 
solution  with  a  pressure  equal  to  the  osmotic  pressure.  With 
such  an  arrangement  the  concentration  of  the  liquid  could 
be  altered  by  increasing  or  decreasing  pressure  by  means  of 
the  piston ;  as  the  process  would  be  reversible,  the  second 
law  of  thermodynamics  may  be  applied. 

Experiments  on  osmotic  pressure  have  been  conducted  by 
de  Vries1,  Pfeffer2,  and  others;  the  results  shew  that  the 
osmotic  pressures  of  dilute  solutions  are  proportional  to  the 
concentrations  of  the  solutions.  Now  the  statement  that  the 
alteration  of  concentration  of  a  dilute  solution  is  proportional 
to  the  pressure  exerted  by  the  solution,  is  equivalent  to  saying 
that  Boyle's  law  holds  good  for  dilute  solutions.  Moreover 
the  proportionality  of  concentration  to  osmotic  pressure  may 
be  theoretically  deduced.  If  we  assume,  as  seems  justifiable, 
that  osmotic  pressure  is  due  to  the  impact  of  the  molecules  of 
the  dissolved  substance,  then  the  number  of  impacts  in  unit 
time  must  be  proportional  to  the  number  of  molecules  in  unit 
volume.  But  this  is  the  molecular  conception  of  the  pressure 
of  a  gas ;  and  as  in  gases  volume  is  inversely  as  pressure,  the 
same  proportionality  should  hold  good  in  dilute  solutions,  in 
other  words,  Boyle's  law  should  apply  to  these  solutions. 

van't  Hofif  then  proceeds  to  deduce,  by  thermodyna-mical 
reasoning,  that  osmotic  pressure  is  proportional  to  absolute 
temperature,  provided  concentration  remains  constant;  this 
conclusion  is  equivalent  to  the  law  of  Charles  for  gases,  inas- 
much as  concentration  in  one  case  corresponds  with  volume 
in  the  other. 

1  See  especially  Zeitschr.  fitr physikcd.  Chemie,  2.  415. 
8  Osmotische  (Jntersiichungen  [Leipzig,  1887]. 

29—2 


45 2  CHEMICAL   CHANGE.  [BOOK  II. 

The  experimental  results  obtained  by  Pfeffer,  and  also 
by  Soret l,  are,  on  the  whole,  in  keeping  with  the  statement 
that  the  laws  of  Boyle  and  Charles  hold  good  in  dilute  solu- 
tions. 

Further  thermodynamical  reasoning  applied  to  isotonic 
solutions,  i.  e.  solutions  exerting  equal  osmotic  pressures, 
leads  to  the  conclusion  that  the  osmotic  pressure  of  a  stated 
mass  of  a  gasifiable  substance  in  dilute  solution  is  equal 
to  the  pressure  exerted  by  the  same  mass  of  the  same  sub- 
stance existing  as  a  gas  at  the  same  temperature.  If  then 
osmotic  pressure  may  be  substituted  for  gaseous  pressure, 
Avogadro's  law  may  be  extended  to  substances  in  dilute  solu- 
tion. This  extension  of  Avogadro's  law  is  thus  stated  by 
van't  Hoff, — "  Equal  volumes  of  different  solutions,  at  the  same 
temperature  and  osmotic  pressure,  contain  equal  numbers  of 
molecules,  which  numbers  are  the  same  as  would  be  contained 
in  equal  volumes  of  gases  at  the  same  temperature  and  pres- 
sure? 

This  is  van't  Hoffs  law  of  osmotic  pressure. 

The  first  experimental  proof  of  the  accuracy  of  this  law  is 
obtained  from  the  results  of  Pfeffer's  experiments  on  the 
osmotic  pressure  of  sugar  solutions  at  different  temperatures, 
,by  comparing  these  with  the  pressures  exerted  at  the  same 
temperatures  by  a  volume  of  hydrogen  containing  the  same 
number  of  molecules  as  the  sugar-solution.  The  second  proof 
of  the  accuracy  of  the  law  is  obtained  by  proving  thermo- 
dynamically  that  the  vapour-pressures  of  solutions  containing 
equal  numbers  of  molecules  of  different  substances  are  equal  ; 
but  this  statement  has  already  been  established  experi- 
mentally by  Raoult  (Compt.  rend.  44.  1431;  87.  167).  The 
third  proof  of  the  accuracy  of  the  law  also  rests  on  thermo- 
dynamical reasoning ;  van't  Hoff  shews  that  solutions  in  the 
same  solvent  having  the  same  freezing  point  are  isotonic, 
i.e.  exert  equal  osmotic  pressures,  at  their  freezing  points ; 
and  from  this  he  deduces  the  conclusion  that  solutions  which 
contain  equal  numbers  of  molecules  in  equal  volumes,  and 


Ann.  Chim.  Phys.  (5)  22.  -293. 


CH.  III.  §235]  OSMOTIC   PRESSURE.  453 

which  are  therefore  isotonic  by  the  law  of  osmotic  pressure, 
have  the  same  freezing  point.  But  this  statement  is  identical 
with  Raoult's  law  of  molecular  lowering  of  freezing  point 
which  was  gained  by  laborious  experimental  investigation 
(v.  Book  I.  par.  35).  This  third  proof  of  the  law  furnishes  a 
convenient  method  for  finding  osmotic  pressures  from  deter- 
minations of  the  lowering  of  freezing  points  of  dilute  solutions. 

But  there  are  many  exceptions  to  Raoult's  law  of  mole- 
cular lowering  of  freezing  point.  These  exceptions  are  ex- 
plained, if  we  assume,  with  Arrhenius,  that  compounds  whose 
behaviour  is  not  expressed  by  this  law  are  partially  disso- 
ciated in  solution.  Here  again  there  is  a  marked  analogy 
between  gases  and  dilute  solutions ;  as  the  pressure  of  ammo- 
nium chloride  vapour  is  greater  than  that  calculated  by 
applying  Avogadro's  law  on  the  assumption  that  the  vapour 
consists  of  molecules  of  NH4C1,  but  as  the  observed  pressure 
agrees  with  the  calculated  pressure  when  it  is  assumed  that 
the  vapour  consists  of  equal  numbers  of  molecules  of  NH8 
and  HC1,  so  the  apparently  abnormal  osmotic  pressures  of 
many  solutions  may  be  reconciled  with  the  law  of  osmotic 
pressure  by  assuming  that  the  compounds  in  these  solutions 
are  more  or  less  dissociated  into  simpler  molecules. 

The  osmotic  pressures  of  certain  solutions  agree  with 
those  calculated  by  van't  Hoff  s  law  from  observations  of  the 
lowering  of  the  freezing  points  of  the  solutions ;  these  solu- 
tions are  generally,  if  not  always,  non-electrolytes.  The 
exceptions  to  the  law  of  van't  Hoff  occur  chiefly,  if  not 
wholly,  among  electrolytes.  The  hypothesis  of  Arrhenius 
(par.  237)  regards  such  electrolytes  as  more  or  less  dissociated 
into  their  ions  when  they  are  dissolved  in  water. 

Dealing  with  exceptions  to  the  law  of  osmotic  pressures, 
van't  Hoff  calculates  the  ratio  of  the  observed  pressures  to 
the  pressures  which  would  be  exerted  did  the  law  fully  express 
the  behaviour  of  the  compounds  in  question.  This  ratio  he 
designates  by  the  symbol  i\  values  are  obtained  for  i  from 
Raoult's  freezing-point  determinations1.  The  law  of  mass- 

1  For  more  recent  and  more  trustworthy  determinations  of  i  for  40  compounds 
v.  Raoult,  Zeitschr.fur  physikul.  Chcmie,  2.  488;  and  Arrhenius,  ibid.  2.  491. 


454  CHEMICAL   CHANGE.  [BOOK  II. 

action  of  Guldberg  and  Waage  is  then  considered  by  van't 
Hoff,  formulae  being  used  in  which  the  ratio  i  occurs ;  the 
results  agree  very  fairly  with  the  calculated  numbers. 

The  law  of  osmotic  pressure  has  been  placed  on  a  fairly 
firm  basis  by  van't  Hoff,  who  has  also  shewn  that  the  hypo- 
thesis that  many  compounds,  and  especially  electrolytes,  are 
partially  dissociated  in  dilute  solutions,  serves  to  explain  many 
if  not  all  the  apparent  exceptions  to  the  law. 

236  Planck,  in  memoirs1  published  independently  of  van't  Hoff, 
by  purely  thermodynamical  reasoning,  arrived  at  the  con- 
clusion that,  in  the  case  of  compounds  which  do  not  obey 
Raoult's  law  of  lowering  of  freezing  point,  van't  Hoff's  co- 
efficient i  expresses  the  ratio  of  the  number  of  molecules 
actually  present  in  solution  to  the  number  which  would 
have  been  present  had  no  dissociation  occurred.  In  other 
words,  Planck  concludes  that  the  observed  phenomena  re- 
garding the  freezing  points  of  dilute  solutions  can  be  brought 
into  accordance  with  thermodynamical  laws  only  by  assuming 
that,  in  many  cases,  dissociation  of  the  molecules  of  the  dis- 
solved body  has  occurred,  and  that  the  ratio  of  the  observed  to 
the  calculated  osmotic  pressure  of  substances  which  do  not 
obey  the  law  of  freezing  points  is  also  the  ratio  of  the  number 
of  molecules  actually  present  to  the  total  number  which  would 
have  been  present  if  dissociation  had  not  occurred. 
237  Arrhenius2  has  developed  the  Clausian  hypothesis  of  elec- 
trolytic dissociation,  and  in  doing  this  he  has  made  use  of 
van't  Hoff's  law  of  osmotic  pressure. 

Arrhenius  applies  the  term  'active'  to  the  molecules  of 
an  electrolyte  which  are  supposed  to  be  dissociated  in  solu- 
tion; the  undissociated  molecules  he  calls  'inactive'.  The 
ratio  between  the  number  of  active  molecules  and  the  sum  of 
all  the  molecules,  whether  active  or  inactive,  is  called  by 
Arrhenius  the  'activity-coefficient'  of  the  solution  (this  is  the 
same  as  the  'dissociation-ratio'  of  Lodge3),  and  is  represented 
by  the  symbol  a.  At  infinite  dilution  all  the  molecules  of  an 

1  Wied.  Ann.  32.  462;  34.  139;  Zeitschr.  fiir  physikal.  Ckemie,  1.  577. 

2  Especially  Zeitschr.  fur  physikal.  Chemie,  1.  631;  2.  284,  491. 

3  Brit.  Ass.  Reports,  1886.  756. 


CH.  III.  §§235 — 237]      ELECTROLYTIC   DISSOCIATION.  455 

electrolyte  are  supposed  to  be  active,  and  therefore  the 
activity-coefficient  is  equal  to  unity;  in  less  dilute  solutions, 
but  still  so  dilute  that  the  effects  of  internal  friction,  &c.  may 
be  overlooked,  the  activity-coefficient  may  be  taken  as  the 
ratio  between  the  observed  molecular  conductivity  and  the 
limiting  value  at  infinite  dilution.  (For  Ostwald's  method  of 
rinding  this  ratio  v.  ante,  pars.  225,  226.)  The  value  of  van't 
Hoff's  coefficient  i  can  be  calculated  if  a  is  known1.  Putting 
m  as  the  number  of  inactive  molecules,  ri  as  the  number  of 
active  molecules,  and  k  as  the  number  of  ions  into  which  each 
active  molecule  is  separable  (e.g.  KC1  is  separable  into  2  ions, 
K  +  Cl,  and  KaSO4  into  3  ions,  K  +  K  +  SOJ,  we  have 

.  _  m  +  k.n  t 
m  +  n  ' 

n 
but  a  =    -     — ; 

m  +  n 

hence  i  =  i  +  (k  —  i)  a. 

Arrhenius  then  calculates  i  from  observations  of  a  for  a  great 
many  compounds ;  he  also  calculates  i  for  the  same  bodies 
from  determinations  of  the  lowering  of  the  freezing  points  of 
solutions  of  these  bodies2.  The  two  series  of  values  for  i  agree 
very  well  on  the  whole.  For  non-conducting  liquids  such  as 
methylic  alcohol,  ethylic  acetate,  &c.,  i  is  approximately 
equal  to  unity ;  for  bases,  acids,  and  salts,  i  varies  from  i  to 
about  2-5. 

We  have  already  seen  (pars.  225,  226)  that  Ostwald's 
measurements  of  the  molecular  conductivities  of  monobasic 
acids  have  led  to  results  in  keeping  with  those  deduced  from 
the  hypothesis  of  electrolytic  dissociation.  In  two  memoirs8, 
Arrhenius  uses  the  same  hypothesis  to  explain  the  conduc- 
tivities of  solutions  of  mixtures  of  different  electrolytes ;  the 

1  See  also  van't  Hoff  and  Reicher,  Zeitschr.fiir physikal.  Chemie,  3.  198. 

2  Let  lowering  of  freezing  point  of  water  produced  by  dissolving  i  gram- 
molecule  of  given  body  in  i  litre  water  =  /;  then  i  =  -^— ;  v.  van't  Hoff,  Phil. 

Mag.,  August,  1888,  p.  100. 

3  Zeitschr.  fur  physikal.  Chemie,  1.  631 ;  2.  284. 


456  CHEMICAL   CHANGE.  [BOOK  II. 

results  obtained  agree  very  closely  with  the  calculated  re- 
sults. To  follow  the  reasoning  here  would  lead  us  too  far 
afield.  One  point  however  must  be  noted ;  Arrhenius  shews 
that  the  hypothesis  enables  the  retarding  influence  of  am- 
monium salts  on  the  saponification  of  ethylic  acetate  by 
ammonia  to  be  quantitatively  determined,  and  that  the 
numbers  theoretically  calculated  agree  well  with  those 
actually  observed.  Arrhenius  also  extends  the  hypothesis  to 
the  case  of  any  number  of  electrolytes  in  solution  together ; 
the  equation  arrived  at1  expresses  the  conditions  of  chemical 
equilibrium  for  a  mixture  of  electrolytes,  and  the  quantitative 
applications  of  this  equation  give  good  results. 

The  work  of  van't  Hoff  and  Arrhenius  establishes  a  large 
probability  in  favour  of  the  statement  that  the  properties  of 
dilute  solutions  can  be  deduced  from  two  principles,  viz.  the 
principle  of  the  close  analogy,  and  in  some  respects  even  the 
agreement,  between  the  gaseous  state  and  the  state  of  dilute 
solution,  and  the  principle  of  electrolytic  dissociation2. 
238  Arrhenius 3  points  out  that  many  physico-chemical  proper- 
ties of  salts  in  solution  can  be  represented  as  approximately 
the  sums  of  the  properties  of  parts  of  the  solution ;  such  pro- 
perties are  the  heats  of  neutralisation  of  acids  by  bases  in 
dilute  solution,  the  specific  volumes  and  specific  gravities,  the 
specific  refractive  powers,  and  the  conductivities,  of  dilute 
solutions  of  salts.  The  fact  that  such  properties  as  these 
are  additive,  as  distinguished  from  cumulative  properties,  is 
entirely  in  keeping  with  the  hypothesis  of  electrolytic  disso- 
ciation, inasmuch  as  this  hypothesis  regards  a  dilute  solution 
of  an  electrolyte  as  composed,  for  the  most  part,  of  the  ions  of 
the  electrolyte,  each  ion  having  its  own  characteristic  properties 
which  are  generally  independent  of  the  properties  of  the  other 

1  Zeilschr.  fur  physikal.  Chemie,Z.  294. 

2  The  agreements  between  the  observed  and  calculated  numbers  do  not,  of 
course,  finally  establish  the  accuracy  of  these  two  principles. 

The  law  of  van't  Hoff  gives  a  means  for  determining  the  molecular  weights 
of.  salts  in  solution ;  but  the  work  of  Arrhenius  points  to  the  existence  in  many 
salt  solutions  of  molecules  of  different  degrees  of  complexity,  and  suggests  that  in 
many  cases  we  cannot  speak  (A  the  molecular  formula  of  a  salt  in  solution. 

3  Ibid.  1.  64o. 


CH.  III.  §§237—  239]      ELECTROLYTIC   DISSOCIATION.  457 

ion.  The  solutions  of  salts  which  have  been  used  for  measure- 
ments of  specific  gravity,  refractive  power,  lowering  of  freezing 
points,  &c.,  have  not,  as  a  rule,  been  so  dilute  as  to  ensure 
complete  dissociation  of  the  dissolved  bodies  ;  hence  the  pro- 
perties mentioned  appear  as  approximately  the  sums  of  certain 
constants,  each  of  which  belongs  to  one  part  of  the  solution. 
When  we  deal  with  fairly  dilute  solutions  of  the  salts  of  strong 
acids  with  strong  bases,  or  with  dilute  solutions  of  the  strong 
acids  and  bases  themselves,  no  large  errors  are  introduced  by 
generally  assuming  that  such  properties  as  those  named  are 
the  sums  of  the  properties  of  the  ions.  The  weak  acids  and 
bases,  and  several  salts  —  e.g.  ammonia  and  the  amines,  phos- 
phoric, boric,  hydrocyanic,  and  sulphhydric,  acids,  and  many 
salts  of  mercury,  cadmium,  and  zinc  —  do  not  appear  to  be 
largely  dissociated  in  solution  ;  the  properties  of  such  com- 
pounds in  solution  are  not  so  distinctly  additive  as  are  the 
properties  of  the  strong  acids  and  bases  and  the  salts  formed 
by  the  interactions  of  these.  It  is  then  necessary  to  distin- 
guish between  different  classes  of  compounds  ;  some  are 
almost  wholly  dissociated  in  dilute  solutions  into  their  ions, 
others  are  partially  dissociated,  and  others  are  dissociated  only 
to  a  small  extent1. 

239  In  par.  229  was  given  a  short  account  of  Ostwald's  applica- 
tion of  the  law  of  osmotic  pressure,  and  the  hypothesis  of 
electrolytic  dissociation,  to  find  the  affinities  of  monobasic 
acids.  The  equation  given  by  Ostwald 


ought  to  express  completely  the  electrical  conductivity  of 
binary  electrolytes,  if  the  hypothesis  of  electrolytic  disso- 
ciation is  well  founded.  Ostwald2  notes  six  generalisations 
regarding  aqueous  solutions  of  binary  electrolytes  which  have 
been  established  empirically.  These  are  :  — 

1  The  degree  of  dissociation  is  determined  from  measurements  of  the  coeffi- 
cients i  and  a  :  v.  pars.  235,  237. 

2  Zeitschr,  fiir  physikal.  CAewie,  2.  275. 


45^  CHEMICAL   CHANGE.  [BOOK  II. 

1.  The  molecular  conductivities  of  solutions  of  electrolytes 
increase  with  increasing  dilution,  and  asymptotically  approach 
maximum  values. 

2.  The   maximum   values   for    equivalent   quantities   of 
acids,  bases,  and  salts,  are  of  the  same  order  but  they  are  not 
identical. 

3.  The  maxima  may  be  expressed  as  sums  of  two  quan- 
tities, one  of  which  depends  only  on  the  positive  ion,  and  the 
other  only  on  the  negative  ion. 

4.  The  last  statement  does  not  hold  good  for  somewhat 
concentrated   solutions,  nor  for   solutions  of  weak  acids  or 
bases. 

5.  The  molecular  conductivities  of  bad  conductors,  such 
as  weak  acids  and  bases,  increase  rapidly  as  dilution  increases; 
the  conductivities  of  monobasic  acids  and  mono-acid  bases  are 
proportional  to  the  square  root  of  the  dilution. 

6.  Increase  of  molecular  conductivity  follows  the  same 
course   in  solutions   of  all  monobasic  acids  and  mono-acid 
bases  ;  the  dilutions  at  which  the  conductivities  of  these  acids 
and  bases  are  equal  fractions  of  their  maximum  conductivities 
bear  a  constant  proportion  to  one  another. 

Ostwald  then  proceeds  to  shew  that  the  equation  already 
given  contains  these  six  generalisations.     The  equation  is 


1*9 


where  /^=  molecular  conductivity  for  volume  v,  //,«,  =  maximum 
conductivity  for  infinite  dilution,  v  =  volume  of  solution. 
i.     If  v  increases  without  limit,  the  expression 


must  approach  zero.  As  both  pv  and  //,»  have  finite  values, 
/itoo  —  /JLV  must  become  smaller,  i.e.  /^will  increase  continuously 
until  it  reaches  the  limiting  value  fj,x. 

2  and  3.  As  //,*,  expresses  the  molecular  conductivity  of 
the  completely  dissociated  electrolyte,  and  as  the  ions  move 
in  this  solution  independently  of  one  another,  the  value  of  //.^ 


CH.  III.  §  239]      ELECTROLYTIC   DISSOCIATION.  459 

can  be  regarded  as  the  sum  of  two  quantities,  which  are 
measured  by  the  velocities  of  the  ions,  quite  apart  from  the 
nature  of  the  compound  which  was  formed  by  the  union  of 
these  ions.  If  compounds  are  compared  which  have  one 
common  ion,  and  the  other  ions  of  which  do  not  shew  great 
differences  in  their  velocities  of  transference,  then  the  sums 
of  the  two  velocities  must  be  of  the  same  order  of  magni- 
tude. 

4.  The  conductivities  of  fairly  concentrated  solutions  are 
conditioned  by  the  degree  of  dissociation  of  the  solutions,  and 
as  this  varies  in  different  solutions,  especially  in  weak  acids 
and   bases,  the   conductivities   of  these  solutions  cannot  be 
expressed  as  the  sums  of  two  quantities  one  of  which  depends 
only  on  each  ion.     Salts,  however,  of  similar  composition  are 
nearly  equally  dissociated  in  solutions  of  equal  dilution  ;  the 
molecular  conductivities  of  such  salts  are  equal  fractions  of 
their  maximum  values,  and  they  can  be  expressed  as  the  sums 
of  two  quantities  which  are  the  velocities  of  the  ions  multiplied 
into  the  degree  of  dissociation. 

5.  In  the  cases  of  weak  acids  and  bases  /*„  is  small  com- 
pared with  /ia,,  and  px  —  pv  is  nearly  constant,  and  the  equa- 
tion gives  nJ  —  v  const.     In  other  words,  when  conductivity  is 
small,  it  increases  proportionately  to  the  square  root  of  the 
dilution. 

6.  In  the  equation,  the  constant  c  depends  on  the  nature 
of  the  electrolyte  ;  if  the  dilutions  at  which  the  relative  con- 
ductivities of  various  electrolytes  are  equal  are  put  as  vt  va  ... 
then  the  values  of 


/*. 

are  equal,  and      vl  :  v^\  va  .  .  .  =  ct  :  ca  :  C3  .  .  .  ; 

i.e.  the  dilution  at  which  the  conductivities  of  different  electro- 
lytes are  equal  bear  a  constant  relation  to  one  another,  and 
this  relation  depends  only  on  the  nature  of  the  electrolytes. 

In  these  six  points  then,  there  is  complete  agreement 
between  the  empirically  determined  data  and  the  deductions 
from  the  equation  which  expresses  the  conductivity  of  binary 
electrolytes.  But  this  equation  is  itself  deduced  from  the 


460  CHEMICAL  CHANGE.  [BOOK  II. 

principles  of  electrolytic  dissociation  and  of  agreement  be- 
tween the  gaseous  state  and  the  state  of  bodies  in  dilute 
solution.  We  have  already  seen  (par.  229)  how  Ostwald  has 
modified  the  equation  expressing  the  behaviour  of  binary 
electrolytes  so  as  to  obtain  measurements  of  the  constant 
which  is  dependent  on  the  nature  of  the  electrolyte.  In  the 
case  of  acids,  this  constant  expresses  the  affinity  of  the  elec- 
trolyte ;  the  agreement  between  the  affinities  of  acids  thus 
determined  and  the  affinities  determined  by  other  physical 
and  chemical  methods,  is  a  further  proof  of  the  trust- 
worthiness of  the  principles  on  which  the  electrical  method 
is  based. 

240  The  hypothesis  of  the  dissociation  of  electrolytes  in  solu- 
tion is  connected  with  van't  Hoff's  extension  to  solutions  of 
the  law  of  Avogadro,  in  much  the  same  way  as  the  hypothesis 
of  gaseous  dissociation  is  connected  with  Avogadro's  law  in 
its  original  form.     Planck's   thermodynamical    investigations 
give  independent  support  to  the  hypothesis.     The  hypothesis 
gives  a  fairly  complete  account  of  the  conductivities  not  only 
of  electrolytes  in  solution,  but  also  of  mixtures  of  electrolytes. 
The  results  of  determinations  of  the  molecular  lowering  of  the 
freezing  points  of  solutions  strikingly  confirm  the  hypothesis, 
and  afford  a  convenient  method  for  determining  the  ratio  of 
the  number  of  molecules  actually  present  to  the  number  which 
would  have  been  present  had  no  dissociation  occurred.     The 
hypothesis  gives  an  explanation  of  the  retarding   influence 
-of  neutral   salts   on   the  rates   of  chemical  actions  brought 
about  by  weak  acids.     From  the  hypothesis   of  electrolytic 
dissociation,    taken  along  with  van't  Hoff's  law  of  osmotic 
pressure,  an  equation  is  deduced  which  enables  measurements 
to  be  made  of  the  affinities  of  acids,  and  these  affinities  are  in 
keeping  with  the  values  obtained  by  wholly  different  methods, 
both  physical  and  chemical1. 

241  If  we  accept  the  law  of  van't  Hoff,  and  the  principle  of 
electrolytic   dissociation,   we  must   regard   the   chemical   re- 
actions of  acids  and  bases  in  solution,  as,  at  any  rate  very 

1  For  a  brief  statement  of  the  present  position  of  the  electrolytic  dissociation- 
hypothesis,  v.  Arrhenius,  Zeitschr.fiirphysikal.  Cheinie,  2.  504  (July,  1888). 


CH.  III.  §§239— 241]      ELECTROLYTIC  DISSOCIATION.  461 

largely,  dependent  on  the  extent  to  which  these  compounds 
are  dissociated  into  their  ions,  and  on  the  velocities  of  trans- 
ference of  these  ions.  Inasmuch  as  hydrogen  moves  so 
much  more  rapidly  than  any  of  the  negative  ions  of  acids, 
the  chemical  reactions  of  acids  in  solution  will  chiefly  depend 
on  the  degree  of  dissociation.  The  exact  form  in  which  this 
conception  is  applied  in  order  to  find  the  affinities  of  acids 
has  been  given  in  par.  229 ;  it  is 


—  m 

— 2— 
m* 


where  ;;/  =  molecular  conductivity  at  any  stated  dilution, 
referred  to  the  maximum  molecular  conductivity,  and  c  =  a 
constant  =  affinity  of  the  acid. 

In  comparing  gaseous  dissociation  with  dissociation  in 
solution,  it  is  important  to  note  that  just  as  all  gases  are  not 
dissociated  by  heat,  so  all  salts,  acids,  and  bases,  are  not 
dissociated  in  solution ;  nevertheless,  if  the  hypothesis  of 
dissociation  is  adopted,  and  the  law  of  van't  Hoff  is  taken 
to  be  true,  the  data  shew  that  dissociation  is  a  much  more 
frequent  occurrence  among  compounds  in  solution  than 
among  gases.  The  compounds  which  most  readily  and  most 
completely  undergo  dissociation  in  solution  are  electrolytes ; 
the  greater  the  conductivity  the  more  complete  is  the  dis- 
sociation. Now  if  a  compound  is  a  good  electrolytic  con- 
ductor it  is  also  ready  to  take  part  in  chemical  reactions. 
The  strong  acids  and  bases— e.g.  HC1,  HNO8,  KOH,  NaOH 
— are  chemically  very  energetic,  and  their  conductivities  are 
very  large.  Hence,  if  we  adopt  the  hypothesis  of  electrolytic 
dissociation,  we  must  regard  the  readiness  shewn  by  the 
strong  acids  and  bases  in  solution  to  exchange  hydrogen  and 
hydroxyl  in  chemical  reactions,  as  due  to  the  large  extent 
to  which  they  are  dissociated  in  solutions,  into  hydrogen  and 
negative  ions  on  the  one  hand,  and  hydroxyl  and  positive 
ions  on  the  other  hand.  At  the  first  glance  it  is  difficult  to 
accept  the  conception  of  such  compounds  as  hydrochloric 
and  nitric  acids,  or  soda  and  potash,  as  existing  in  solution 
dissociated  into  their  ions.  But  some  of  the  difficulty  arises, 


462  CHEMICAL   CHANGE.  [BOOK  II. 

as  Ostwald  points  out1,  partly  from  confounding  the  affinities 
which  hold  together  the  elements  of  a  compound  with  the 
affinity  which  this  compound  exhibits  towards  other  bodies, 
and  partly  from  forgetting  that  the  ions  of  an  electrolyte 
which  is  dissociated  in  solution  are  not  comparable  with  the 
same  bodies  in  the  free  state,  because  the  ions  carry  with 
them  enormous  electrical  charges2.  Because  potassium  hydr- 
oxide is  chemically  extremely  energetic,  it  does  not  follow 
that  '  the  elements  are  held  together  in  this  compound '  as 
is  sometimes  said  '  by  the  strongest  affinities.'  The  reverse 
of  this  rather  is  true :  it  is  in  compounds  which  do  not 
readily  enter  into  chemical  reactions,  such  as  the  paraffins 
and  their  derivatives,  that  the  elements  are  firmly  held  by 
strong  affinities. 

To  meet  the  objection  that  we  cannot  suppose  a  solution 
of  potash  to  contain  the  ion  potassium,  because  we  know 
that  potassium  and  water  at  once  react  to  form  hydrogen 
and  potash,  Ostwald  brings  forward  the  following  considera- 
tions3. Let  two  glass  vessels  contain  potassium  chloride 
solution ;  let  the  vessels  be  brought  into  communication  by 
a  glass  tube  filled  with  the  same  solution ;  now  let  a  nega- 
tively electrified  body  be  brought  near  one  of  the  vessels, 
the  contents  of  this  vessel  become  positively  electrified  and 
those  of  the  other  vessel  become  negatively  electrified ;  let 
the  connecting  tube  be  now  removed,  and  then  let  the  nega- 
tively electrified  body  be  removed;  the  contents  of  the  vessels 
remain  electrified,  one  positively  and  the  other  negatively. 
Now,  according  to  Faraday's  law,  electricity  must  travel  in 
an  electrolyte  with  the  ions  ;  therefore  the  vessel  which 
remains  positively  electrified  must  have  positively  electrified 
potassium  atoms  accumulated  in  it,  while  negatively  electrified 
atoms  of  chlorine  must  have  accumulated  in  the  other  vessel. 
If  a  platinum  wire,  in  connexion  with  the  earth,  is  now 

1  Zeitschr.furphysikal.  Chemie.  2.  270. 

2  It  is  to  be  remembered  that  the  statement,  that  the  ions  of  an  electrolyte 
are  endowed  with  electrical   charges  and  are  thus  different  from  the  products 
of  dissociation  of  a  gas,  does  not  explain  the  difference  in  question,  because  we 
are  as  yet  ignorant  what  an  electrical  charge  is. 

3  Loc.  cit.  pp.  271—273. 


CII.  III.  §  241]      ELECTROLYTIC   DISSOCIATION.  463 

brought  into  the  positively  electrified  vessel,  potash  and 
hydrogen  are  produced;  and  this  is  because  the  atoms  of 
potassium  give  up  their  electric  charges  and  then  at  once 
interact  with  the  water. 

From  this  experiment,  Ostwald  draws  the  conclusion  that 
the  electrolyte  must  have  been  dissociated  in  the  solution 
before  the  electrified  body  was  brought  near.  The  measure- 
ments of  Kohlrausch  shew  that  the  rates  at  which  ions  travel 
may  be  stated  in  not  very  many  millimetres  per  second  ;  but 
electrolytes  take  up  electrostatic  charges  practically  instan- 
taneously ;  hence,  in  the  experiment  described,  the  chlorine 
atoms  which  accumulate  in  one  vessel  could  not  have  been 
originally  in  combination  with  the  potassium  atoms  which 
appear  in  the  other  vessel.  A  similar  conclusion  is  drawn1 
from  the  results  of  the  common  experiment  of  placing  amal- 
gamated zinc  and  a  platinum  wire,  at  a  considerable  distance 
apart,  in  dilute  sulphuric  acid,  and  then  connecting  the  zinc 
and  platinum.  Hydrogen  instantly  appears  on  the  platinum ; 
but  this  hydrogen  cannot  have  been  in  combination  with  the 
negative  ion,  SO4 ,  which  at  the  same  moment  combines  with 
the  zinc,  because  the  rates  at  which  the  ions  hydrogen  and 
SO4  travel  during  electrolysis  are  not  rapid  enough  to  have 
enabled  the  hydrogen  to  pass  to  the  platinum  and  the  SO4  to 
pass  to  the  zinc8. 

The  affinity-coefficients  of  the  acids  and  bases  in  solution 
are  then,  on  this  hypothesis,  measures  of  the  dissociation  of 
these  compounds ;  and  as  the  amount  of  dissociation  of  an 
acid  or  base  is  generally  independent  of  the  body  with  which 
the  acid  or  base  chemically  reacts,  these  affinity-coefficients 
have  constant  values  which  depend  only  on  the  nature  of  the 
acid  or  base.  If  however  another  body  should  be  present 
which  modifies  the  dissociation  of  the  acid  or  base,  the  pre- 
sence of  this  body  will  also  modify  the  affinity  of  the  acid  or 
base.  This  explains  the  fact  that  the  affinities  of  the  acids  are 
modified  by  the  presence  of  the  normal  salts  of  these  acids8. 

1  Zeitschr.  fitr  physikal.  Chetnie,  2.  pp.  271 — 273. 

5  See  also  Ostwald  and  Nernst,  Zeitschr.  fur  physikal.  Chemie,  3.  1 10. 

3  Arrhenius  has  worked  out  in  detail  the  modifying  influence  of  normal  salts, 


464  CHEMICAL   CHANGE.  [BOOK  II. 

As  the  molecular  conductivities  of  the  acids  depend  on  the 
degree  of  dissociation  of  the  acids,  and  also  on  the  velocities 
of  transference  of  their  ions,  but  chiefly  on  the  former  because 
the  positive  ion  hydrogen  travels  more  than  five  times  more 
rapidly  than  the  quickest  travelling  negative  ion,  so  the 
affinities  of  acids  depend  on  the  degree  of  dissociation  of  these 
acids  and  on  the  velocities  of  transference  of  their  ions. 

But  the  affinities  are  dependent  on  the  velocities  of  the 
ions  to  a  greater  extent  than  the  conductivities.  In  some 
reactions,  e.g.  the  solution  of  zinc  in  acids,  the  velocity  of  the 
negative  ion  plays  an  important  part ;  in  such  cases  the  action 
of  acids  which  are  all  equally  dissociated  will  vary  in  accord- 
ance with  the  velocities  of  their  negative  ions.  In  other 
reactions  the  negative  ion  will  be  of  little  importance ;  in 
these  cases  the  actions  of  different  acids  which  are  equally 
dissociated  will  be  equal.  Generally  speaking,  the  readiness 
with  which  acids  react  chemically  will  be  chiefly  dependent 
on  the  degree  of  dissociation  of  the  acids,  because  the  positive 
ion  hydrogen  travels  so  much  more  rapidly  than  the  negative 
ions,  and  the  nature  of  the  negative  ion  will  be  of  secondary 
importance1. 

242  The  hypothesis  sketched  in  the  preceding  paragraphs, 
whether  accepted  or  not,  presents  a  general  conception  of 
those  chemical  changes  which  take  place  between  electrolysable 
bodies  in  solution.  All  compounds  which  in  solution  react 
chemically  with  electrolytes  are  regarded  by  the  hypothesis 
as  themselves  electrolytes. 

It  is  necessary  to  observe  that  the  hypothesis,  in  its  pre- 
sent form  at  any  rate,  is  applicable  only  to  substances  in 
solution.  If  we  regard  the  hydrogen  chloride  in  a  dilute 
aqueous  solution  of  this  compound  as  dissociated  to  the  ex- 
tent of  about  90  per  cent,  and  if  we  assign  the  chemical 
activity  of  the  compound  in  this  solution  to  the  large  prepon- 
derance of  'active'  over  'inactive'  molecules  (i.e.  by  hypo- 
thesis, the  preponderance  of  dissociated  over  undissociated 

and  has  shewn  that  the  amount  of  modification  can  be  correctly  deduced  from  the 
hypothesis  of  electrolytic  dissociation;  v.  Zeitschr.  fiir  physikal.  Chemie,  2.  284. 
1  Ostwald,  Zeitschr.  fiir physikal.  Chemie,  2.  273—275. 


CH.  III.  §§241— 243]      ELECTROLYTIC   DISSOCIATION.  465 

molecules),  it  does  not  follow  either  that  liquid  hydrogen 
chloride  should  be  chemically  active,  or  that  gaseous  hy- 
drogen chloride  should  be  easily  dissociated  by  heat.  The 
hypothesis  does  not  afford  means  for  comparing  the  chemical 
activity,  or  the  stability,  of  gaseous  or  liquid  compounds  with 
the  activity  of  the  same  compounds  when  in  solution. 

It  should  also  be  remembered  that  the  hypothesis  does 
not  assert  the  occurrence  of  dissociation  in  solutions  of  all 
compounds  ;  it  distinguishes  between  non-electrolytes,  solu- 
tions of  which  it  regards  as  not  dissociated,  and  electrolytes, 
which  it  looks  on  as  more  or  less  dissociated  in  solution  ;  and 
it  allows  a  gradation  from  one  class  to  the  other. 
:3  The  action  of  the  solvent  on  the  electrolyte  dissolved  in 
it  is  not  yet  fully  explained  by  the  hypothesis  of  electrolytic 
dissociation.  The  law  of  van't  Hoff  assumes  that  the  volume 
of  the  solvent  is  occupied  by  the  molecules  of  the  dissolved 
body  in  the  gaseous  state.  The  molecules  of  those  compounds 
which  are  apparent  exceptions  to  this  law  are  supposed  to  be 
dissociated  ;  in  these  cases,  the  volume  of  the  solvent  there- 
fore contains  more  molecules  than  if  dissociation  had  not 
occurred,  and,  as  a  consequence,  the  osmotic  pressure  exceeds 
that  calculated  from  the  law.  This  explanation  regards  the 
solvent  as  in  some  way  bringing  about  dissociation  »vithout 
itself  being  changed.  If  the  solvent  acts  merely  as  a  medium 
in  which  the  dissolved  electrolyte  is  dissociated,  one  would 
expect  the  amount  of  dissociation  of  an  electrolyte  to  be 
independent  of  the  composition  of  the  solvent.  But  experi- 
ments shew  that  the  conductivities  of  certain  salts  dissolved 
in  alcohol  are  considerably  less  than  those  of  the  same  salts 
dissolved  in  water1;  Arrhenius  says2  that  this  decrease  in 
conductivity  is  probably  due  to  the  friction  which  the  ions 
must  overcome  being  increased  by  the  substitution  of  alcohol 
for  water. 

Armstrong3  seems   to   think   that   a   non-conductor,  say 

1  Fitzpatrick,  B.  A.  Reports,  1886.   333. 

2  See  B.  A.  Reports,  1888;  "  On  Electrolysis  in  its  Physical  and  Chemical 
Bearings." 

8  See  the  Reports  of  the  B.  A.  Committee  on  Electrolysis,  1886—89. 
M.  C.  30 


466  CHEMICAL  CHANGE.  [BOOK  II. 

liquid  hydrogen  chloride,  is  composed  of  complex  molecular 
aggregates,  which  are  broken  down  by  the  action  of  the  solvent 
into  simple  molecules;  that  these  molecules  flow  past  one 
another,  and  that  although  their  parts  '  strain  at  one  another,' 
yet  the  molecules  are  not  separated  into  their  ions  until  elec- 
tromotive force  is  applied.  The  objection  to  this  view  lies  in 
the  fact  that,  so  far  as  accurate  experiment  has  gone,  electro- 
lytes obey  Ohm's  law,  in  other  words,  that  electrolytes  cannot 
resist  the  smallest  electromotive  force  directly  applied  to  them. 
This  fact  seems  to  require  the  presence  of  some  ions  in  the 
solution  of  an  electrolyte  before  the  current  passes. 

How  then  are  these  ions  produced  ?  Energy  must  be 
obtained  somewhere  to  effect  the  separation  of  the  molecules 
of  the  electrolyte  into  ions.  It  may  be  that  the  water  used  as 
a  solvent  is  chiefly  composed  of  aggregates  of  molecules,  but . 
that  some  molecules,  H2O,  are  also  present,  and  that  the 
combination  of  these  with  molecules  of  the  electrolyte  is  the 
source  of  the  energy  whereby  some  of  the  electrolytic  mole- 
cules are  separated  into  their  ions1. 

Molecular  aggregates  are  probably  formed  before  electro- 
lytic dissociation  begins  ;  in  our  present  ignorance  of  inter- 
atomic forces,  it  seems  enough  to  say  that  the  production  of 
molecular  aggregates  brings  the  atoms  into  intra-molecular 
relations  which  result  in  new  arrangements  of  these  atoms2. 
Or,  it  may  be  said  that  'the  molecular  aggregates  in  solution' 
have  '  an  aptitude  for  directed  decomposition,'  and  that  when 
the  current  is  applied,  electrolysis  results  (Lodge). 
244  There  can  be  no  doubt  of  the  existence  of  a  marked 
parallelism  between  the  electrical  conductivities  and  the 
chemical  activities  of  many  compounds  in  solution.  If  the 
former  is  connected  with  dissociation,  however  effected,  the 
latter  is  probably  due  to  the  same  cause.  As  pure  liquid 
hydrogen  chloride  is  an  extremely  bad  conductor,  if  not 
indeed  non-conductive,  so  is  this  compound  very  inactive 
chemically;  the  addition  of  water  is  accompanied  by  the 

1  Cf.  Pickering,  C.  S.  Journal,  Trans.  1889.  23. 

2  Some  such  view  as  this  seems  to  be  favoured  both  by  Lodge  and  Armstrong. 
See  B.  A.  Electrolysis  Committee  Reports. 


CH.  III.  §§  243,  244]      ELECTROLYTIC   DISSOCIATION.  467 

manifestation  of  conductivity  and  chemical  activity.  We 
cannot  yet  fully  explain  why  the  presence  of  water  so  largely 
changes  the  properties  of  the  hydrogen  chloride ;  but  we 
know  other  cases  wherein  the  presence  of  a  third  body  is 
required  before  chemical  action  takes  place  between  two 
bodies. 

Perfectly  dry  chlorine  and  hydrogen  do  not  combine  in 
sunlight;  the  presence  of  a  very  small  quantity  of  water 
suffices  to  start  the  combination1.  A  mixture  of  perfectly  dry 
carbon  monoxide  and  oxygen  is  not  exploded  by  an  electric 
spark  which  at  once  produces  explosion  if  the  gases  are 
slightly  moist2.  Dry  hydrogen  chloride  is  unchanged  when 
mixed  with  dry  oxygen  and  exposed  to  sunlight,  but  in  the 
presence  of  a  little  liquid  water  chlorine  is  produced  ;  if  the 
water  present  is  all  gaseous,  chemical  action  does  not  occur3. 
A  mixture  of  dry  hydrogen  iodide  and  oxygen  is,  however, 
said  to  be  changed  in  sunlight3. 

Whether  the  water  in  these  reactions  acts  by  directly 
decomposing  one  of  the  gases,  e.g. 

(i) 
(2) 

or  whether  a  compound  of  the  water  with  the  reacting  bodies 
is  first  formed,  e.g. 

OH2OCO  OH2OCO 

W    O  H2OCO          ()    OH2OCO' 

cannot  yet  be  decided4.  The  presence  of  water  is  required  in 
order  to  render  the  molecules  of  the  other  bodies  active. 

Whether  we  accept  the  hypothesis  of  electrolytic  disso- 
ciation or  not,  we  must  admit  that  the  conductivities  and 
chemical  activities  of  many  compounds  are  much  increased 
by  solution  in  water.  If  we  say  that  many  of  the  molecules 
of  the  dissolved  body  acquire  'an  aptitude  for  directed  decom- 

1  Pringsheim,  Wied.  Ann.  32.  384. 

2  Dixon,  Phil.  Trans.  1884.  617;  and  C.  S.  Journal,  49.  94. 

3  Richardson,  C.  S.  Journal,  51.  80 1. 

4  Cf.  Dixon,  l.c.  with  Armstrong,  C.  S.  Journal,  49.  112. 

30—2 


468  CHEMICAL   CHANGE.  [BOOK  II 

position',  and  if  we  agree  to  call  these  molecules  'active',  then 
the  ratio  of  active  to  inactive  molecules  is  the  chief  condition 
which  quantitatively  affects  the  electrical  conductivity  and 
the  chemical  activity  of  the  compound  in  solution.  Ostvvald 
has  shewn  us  how  to  put  this  conception  of  chemical  change 
between  electrolytes  in  solution  into  a  form  which  enables 
constant  values  to  be  found  for  the  affinities  of  these  electro- 
lytes (par.  229). 

245  There  are  definite  connexions  between  the  affinities,  and 
the  composition,  of  acids  (pars.  231-233).  To  trace  definite 
connexions  between  composition  and  properties  has  always 
been  the  aim  of  chemistry.  The  study  of  composition  has  ad- 
vanced further  than  the  study  of  properties.  The  connexions 
between  composition  and  properties  have  been  quantitatively 
investigated  only  in  a  few  cases.  Great  difficulties  attend 
the  elucidation  of  the  connexions  between  the  composition 
and  the  properties  of  bodies:  some  properties,  such  as  weight, 
are  purely  additive;  the  weight  of  a  body  is  the  sum  of  the 
weights  of  its  parts;  other  properties  are  purely  cumulative,  they 
are  dependent  on  the  mode  of  combination  of  the  parts  and  are 
wholly  independent  of  the  nature  and  number  of  these  parts ; 
the  volume  occupied  by  gaseous  molecules  under  standard 
conditions  belongs  to  this  category,  the  volume  is  independent 
of  the  nature  and  number  of  the  atoms  provided  these  are 
all  chemically  combined ;  but  many  properties,  including 
most  chemical  properties,  are  constitutive,  i.e.  they  depend  not 
only  on  the  number  of  the  parts  but  also  on  their  nature  and 
relative  arrangement;  such  properties  as  boiling  point,  crystal- 
line form,  and  specific  rotatory  power,  belong  to  the  category 
of  constitutive  properties1.  The  affinities  of  acids  and  bases 
are  dependent  on  the  constitutions  of  these  compounds.  Each 
acid,  and  each  base,  has  its  own  affinity-coefficient.  If  the 
change  of  constitution  in  the  passage  from  one  of  two  acids 
to  the  other  were  identical  with  the  change  of  constitution  in 
the  passage  from  one  of  a  second  pair  of  acids  to  the  other, 
the  difference  between  the  affinities  of  the  first  pair  of  acids 

1  Ostwald,  v.  especially  KonigL  Scichsischen  Gesellschaft  der  Wissenschaften 
(math.  phys.  Classe)  Bd.  26.  [1889]  237. 


CH.  III.  §§  244— 246]      AFFINITY   AND   VALENCY.  469 

would,  almost  certainly,  be  identical  with  the  difference  be- 
tween the  affinities  of  the  second  pair  of  acids ;  but  such  a 
case  probably  never  occurs. 

The  chemists  who  have  studied  the  subject  of  affinity 
have  belonged  either  to  the  school  of  Bergmann  or  to  that  of 
Berthollet.  To  Ostwald,  more  than  to  any  other  chemist, 
belongs  the  signal  honour  of  finding  the  middle  course,  which, 
neglecting  the  work  of  neither  of  these  great  naturalists, 
leads  to  a  well-founded  and  consistent  method  of  measuring 
affinities,  and  points  the  way  to  the  elucidation  of  the  funda- 
mental problem  of  chemistry.  Bergmann  taught  that  every 
body  has  a  definite  affinity,  and  in  this  he  was  doubtless 
right ;  he  also  taught  that  the  contest  of  affinities  always  leads 
to  the  occurrence  of  chemical  change  in  one  direction  only,  in 
this  he  was  certainly  wrong.  Berthollet  was  right  in  asserting 
that  chemical  change  is  quantitatively  conditioned  by  the 
relative  masses  of  the  reacting  bodies ;  but  his  view  that  the 
affinities  between  acids  and  bases  are  inversely  proportional 
to  the  equivalent  weights  of  these  bodies  is  not  in  keeping 
with  recent  research.  (Ostwald.) 

246  But  we  have  not  yet  gained  a  complete  theory  of  chemical 
change.  Such  a  theory  must  shew  us  what  chemical  con- 
stitution means,  and  it  must  quantitatively  generalise  the 
relations  of  constitution  to  properties.  In  doing  this,  the 
theory  must  bring  into  one  point  of  view  the  scattered  partial 
hypotheses  which  at  present  are  so  numerous  in  chemistry. 
The  theory  must,  for  instance,  connect  the  valencies  of  atoms 
with  the  other  properties  of  atoms,  and  with  the  properties  of 
molecules.  To  do  this  requires  a  conception  of  valency  more 
exact  and  at  the  same  time  wider  than  we  have  at  present, 
and  a  more  thorough  elucidation  of  the  way  in  which  the 
stabilities  of  molecules  are  connected  with  the  valencies  of 
their  atoms. 

While  holding  that  it  is  better  at  present  to  limit  discus- 
sions about  atomic  valencies  to  data  obtained  from  the  com- 
positions and  reactions  of  gaseous  molecules,  I  am  of  opinion 
that  much  progress  will  not  be  made  in  our  knowledge  of 
the  constitution  of  compounds,  and  the  connexions  between 


470  CHEMICAL   CHANGE.  [BOOK  II. 

constitution  and  properties,  unless  the  chemical  properties 
of  bodies  in  solution,  and  of  solid  bodies,  are  carefully  and 
exhaustively  examined.  The  study  of  valency,  and  the 
study  of  affinity,  overlap ;  yet  I  do  not  think  that  the  study 
of  either  will  be  materially  advanced  by  confusing  one  with 
the  other1.  The  composition  of  the  molecules  of  a  certain 
gaseous  compound  is  known,  and  the  valency  of  each  atom  in 
the  gaseous  molecule  is  also  known ;  but  when  the  compound 
is  dissolved  in  water,  or  when  it  is  solidified,  the  interatomic 
relations  may  be,  and  in  many  cases  most  probably  are, 
modified,  so  that  the  molecules  are  able  to  take  part  in 
chemical  changes  which  could  not  be  brought  about  by  the 
gaseous  molecules.  The  cause  of  the  chemical  reactions  of 
the  molecules,  in  both  cases,  we  call  affinity ;  the  number  of 
atoms  with  which  any  specified  atom  is  directly  associated  in 
one  of  the  gaseous  molecules  is  called  in  this  book  the 
valency  of  that  atom  in  that  molecule.  It  may  be  that  the 
electrical  charges  of  the  atoms  are  not  fully  neutralised  in  the 
gaseous  molecules  (whatever  this  may  mean),  but  that  the 
residual  charges  do  not  suffice  to  hold  together  a  greater 
number  of  atoms  than  that  constituting  these  molecules,  and 
that  on  solution,  or  solidification,  these  residual  charges  are 
able  loosely  to  bind  together  complex  molecular  aggregates 
the  atoms  in  which  are  brought  into  such  intra-molecular 
relations  that  new  atomic  arrangements  result,  and  so  new 
compounds  are  formed2.  If  something  of  this  kind  occurs, 
we  should  expect  to  find  series  of  bodies  ranging  from 
mixtures  to  definite  and  stable  compounds.  Let  two  mole- 
cules, one  composed  of  atoms  ab,  and  the  other  of  atoms 
cdy  be  brought  together;  the  (hypothetical)  residual  electric 
charges  may  just  suffice  to  form  an  aggregate  ab .  cd,  wherein 
the  properties  of  the  constituent  molecules,  or  radicles,  ab  and 
cd,  are  recognisable,  although  they  are  to  some  extent  merged 


1  There  is  an  interesting  paper  on  The  thermal  phenomena  of  neutralisation, 
by  Pickering  in  C-  S.  Journal,  51.  593 ;  the  reasoning  seems  to  me  sometimes  to 
be  marred  by  confusing  together  valency  and  affinity. 

2  This  view,  or  a  view  resembling  this,  seems  to  be  favoured  by  Armstrong 
(see  Proc.  R.  S.  1886.  268;  also  Pickering). 


CH.  III.  §§  246,  247]      AFFINITY   AND   ENERGY.  4/1 

in  those  of  the  new  body;  or  the  residual  charges  may  suffice 
to  cause  a  rearrangement  of  the  atoms  with  production  of  the 
new  molecule  abed;  or  lastly  an  exchange  of  atoms  may  occur 
resulting  in  the  formation  of  two  new  molecules  ac  and  bd. 
In  the' first  case  two  different  substances  would  be  obtained, 
according  as  we  started  with  ab  and  cd,  or  with  ac  and  bd\ 
but  in  the  second  case  the  same  body  would  be  produced 
whether  ab  reacted  with  cd  or  ac  with  bd:  which  reaction 
should  occur  would  depend  on  the  affinities  of  the  reacting 
bodies  rather  than  on  the  valencies  of  the  atoms1. 
247  A  complete  theory  of  chemical  change  must  elucidate  and 
accurately  set  forth  the  connexions  between  changes  of  pro- 
perties, changes  of  constitution,  and  changes  of  energy. 

In  Book  I.  we  learned  that  the  primary  object  of  thermal 
chemistry  is  to  measure  the  changes  of  energy  which  accom- 
pany definite  changes  of  composition.  We  found  that  de- 
finite quantities  of  energy  change  form  in  the  passage  from 
one  isomeride  to  another  (pars.  85 — 89).  No  discussion  was 
attempted  in  these  paragraphs  of  the  relations  between 
thermal  changes  and  affinity,  or  between  thermal  changes 
and  chemical  equilibrium. 

A  word  or  two  must  now  be  said  on  this  subject. 

The  heats  of  neutralisation  of  most  acids  in  aqueous 
solution  are  independent  of  the  nature  of  the  base  used,  and 
the  heats  of  neutralisation  of  very  many  bases  are  inde- 
pendent of  the  nature  of  the  acid  used  ;  hence  it  follows  that 
the  heats  of  formation,  in  solution,  of  two  similar  salts  of 
different  metals  differ  by  a  constant  quantity  which  is  in- 
dependent of  the  nature  of  the  acidic  radicles  of  the  salts  * ; 
or  it  may  be  said  that  the  heat  of  formation  of  a  salt,  in 
aqueous  solution,  is  the  sum  of  two  constants,  one  of  which 
belongs  to  the  basic,  and  the  other  to  the  acidic,  radicle. 
Arguing  on  these  lines,  Lothar  Meyer3  arrives  at  the  con- 

1  See  Atkinson's  experiments  (C.  S.  Journal,  1885.  12 2),  described  in  par.  102. 

3  This  is  a  development  of  the  statement  of  the  thermoneutrality  of  salts  first 
laid  down  by  Hess  in  1842;  Pogg.  Ann.  52.  79.  Among  more  recent  papers  on 
the  subject,  see  Pickering,  C.  S.  Journal,  51.  593. 

3  Zeitschr.  fiir  physikal.  Ckemie,  1.  134  (Translation  in  Phil.  Mag.,  June,  1887). 


4/2  CHEMICAL   CHANGE.  [BOOK  II. 

elusion,  that  the  heat  produced  in  the  formation  of  a  salt  is  a 
consequence  of  the  change  of  state  which  the  substances 
undergo,  and  that  it  is  not  conditioned  by  the  mutual  actions 
of  the  constituents,  i.e.  in  ordinary  chemical  language,  by  the 
affinity  of  one  constituent  for  the  other.  Although  each  acid 
and  each  base  has  a  definite  thermal  constant  which  quanti- 
tatively conditions  the  thermal  phenomena  accompanying 
the  formation  of  salts  by  that  acid  or  base,  and  although  each 
acid  and  base  has  also  a  definite  affinity-constant  which 
quantitatively  conditions  its  salt-forming  reactions,  never- 
theless, according  to  Meyer's  view,  the  thermal  constant 
does  not  measure  the  affinity-constant.  Meyer  regards  each 
substance  as  having  a  definite  quantity  of  available  energy 
which  is  increased  or  diminished  by  every  change  of  state ; 
one  of  those  changes  in  which  the  available  energy  is  dimi- 
nished takes  place  when  an  acid  and  a  base  react  to  produce 
a  salt ;  but  the  degradation  of  energy  which  accompanies  this 
change  of  composition  is  not  the  cause,  but  rather  the  con- 
sequence, of  the  mutual  action  of  the  acid  and  the  base ;  the 
cause  of  the  change  we  call  affinity;  it  is  dependent  on  the 
relations  of  the  reacting  bodies ;  but  the  degradation  of  the 
energy  of  each  body  is  dependent  only  on  the  nature  of  that 
body  and  on  the  change  of  state  which  it  undergoes,  and  is 
independent  of  the  nature  of  the  other  body  by  the  presence 
of  which  the  change  of  state  is  rendered  possible. 

The  conclusions  drawn  by  Meyer  may  be  too  sweeping. 
The  heats  of  formation  of  salts,  even  in  aqueous  solution,  are 
the  algebraical  sums  of  many  thermal  changes  which  as  yet 
we  cannot  disentangle.  But,  granting  this,  we  have  a  large 
probability  in  favour  of  the  statement  that  the  heats  of  for- 
mation of  many  salts,  when  the  physical  conditions  are  kept 
as  constant  as  possible,  can  be  represented  as  the  sum  of  two 
constants,  one  of  which  belongs  to  the  basic  radicle  and  one 
to  the  acidic  radicle,  of  the  salts.  This  statement  enables  us, 
I  think,  to  say  distinctly  that  the  affinities  of  acids  and  bases 
are  not  measured  by  the  quantities  of  heat  produced  in  their 
reactions,  unless  indeed  we  use  the  term  affinity  as  synony- 
mous with  potential  energy  of  a  body,  and  we  assume  that 


CH.  III.  §247,  248]       AFFINITY   AND    ENERGY.  473 

the  heat  produced  in  a  reaction  of  this  body  with  another 
measures  the  total  change  of  potential  energy  into  kinetic 
energy. 

If  we  adopt  the  general  conception  of  chemical  change 
between  electrolytes  in  solution  afforded  by  the  hypothesis  of 
electrolytic  dissociation,  we  should  picture  to  ourselves  the 
ions  of  two  electrolytes  as  giving  up  their  electric  charges 
and  so  combining  to  form  a  new  compound  ;  supposing,  for 
simplicity,  each  ion  to  be  an  elementary  atom,  we  should 
regard  the  valencies  of  the  ions  as  determining  the  number  of 
atoms  which  combine  to  form  the  molecule  of  the  new  com- 
pound ;  we  should  say  that  the  cause  of  the  union  is  to  be 
found  in  the  affinities  of  the  ions,  but  what  this  affinity  is  we 
do  not  know ;  and  we  should  look  on  the  quantity  of  heat 
produced  as  to  some  extent  measuring  the  energy  degraded 
in  the  process.  On  this  view,  affinity  is  not  identical  with 
potential  energy1.  The  stability  of  the  new  compound  is  de- 
termined by  the  condition  that  the  entropy  of  the  system 
shall  be  a  maximum  ;  but  the  measurement  of  the  heat  pro- 
duced is  not  a  complete  determination  of  the  change  of 
entropy,  for  entropy  is  a  quantity  of  heat  divided  by  a 
temperature,  and  changes  of  entropy  may  be  conditioned  by 
changes  other  than  thermal.  (See  par.  191.) 

If  we  assert  that  the  quantity  of  heat  produced  in  a  re- 
action measures  the  affinities  of  the  interacting  bodies,  and 
the  affinities  quantitatively  condition  the  direction,  and  the 
amount,  of  the  chemical  change,  we  must  turn  our  backs  on 
the  results  gained  by  Guldberg  and  Waage,  Ostwald,  and 
many  other  chemists,  regarding  the  distribution  of  the  inter- 
acting bodies  in  the  changes  which  occur  when  acids  and 
bases  are  mixed  in  equivalent  quantities. 

248  But  surely  there  must  be  some  connexion  between  the 
quantity  of  heat  produced  in  a  chemical  change  and  the 
electromotive  force  of  the  arrangement. 

1  The  kinetic  theory  of  gases  obliges  us  to  regard  the  atoms  of  a  molecule  as 
in  continual  motion;  the  affinity  of  atoms  cannot  be  looked  on  as  altogether 
potential  energy.  (There  is  an  interesting  paper  by  Pringsheim  in  Ztitschr.  fur 
pkysikal.  Chcmie,  3.  145.) 


474  CHEMICAL   CHANGE.  [BOOK  II. 

In  the  course  of  his  applications  of  the  conception  of  the 
conservation  of  energy,  Joule  undertook  a  series  of  researches 
on  the  '  energetics '  of  the  electric  current 1.  The  case  of  the 
passage  of  a  current  through  a  wire  was  considered,  and  the 
quantity  of  heat  produced  was  found  to  be  expressed  by  the 
equation 

H=CE, 

where  H  is  the  quantity  of  heat  developed  per  second,  and 
C  and  E  are  the  current  and  the  electromotive  force  re- 
spectively. 

Since  Joule  had  himself  shewn  that  heat  is  changeable 
into  work,  the  equation  took  the  form 

W=JH=CE, 

where  J  =  the  mechanical  equivalent  of  heat. 

The  phenomena  attending  the  production  of  heat  during 
the  passage  of  a  current  through  an  electrolyte  were  then 
examined  by  Joule,  and  it  was  shewn  that  the  total  quantity 
of  heat  could  be  separated  into  two  parts.  One  part  was 
expressible  as  the  result  of  overcoming  ordinary  resistance,  in 
accordance  with  his  previous  law,  and  the  other  part  was  due 
to  chemical  changes  in  the  cell.  He  then  determined  the 
quantity  of  heat  produced,  during  a  given  time,  in  a  process 
of  electrolysis  by  a  current  of  given  strength ;  then,  by  ap- 
plying Ohm's  law,  and  the  law  stated  connecting  heat  with 
resistance  and  current,  he  found  the  heat  which  would  have 
been  produced  had  a  wire  with  resistance  equal  to  that  of 
the  electrolyte  been  substituted  for  the  electrolyte.  The 
difference  between  these  two  quantities  of  heat  is,  Joule  said, 
'  equivalent  to  the  heat  which  is  due  to  the  reverse  chemical 
combination  by  combustion  or  other  means '  (loc.  cit.  (2)  3. 
494)- 

The  problem  was  further  considered  by  Sir  W.  Thomson  *. 
His  reasoning  was  somewhat  as  follows. 

1  Phil.  Mag.  20.   98;   22.  204;  and  do.    (2)  3.   481.     See  also  the  article 
'  Electricity'  in  Encycl.  Brit.  Vol.  8.  (gth  Ed.)  pp.  88-92. 

2  Phil.  Mag.  for  December,   1851;   see  Mathematical  and  Physical  Papers, 
1.  472. 


CH.  III.  §§248,  249]  ELECTROMOTIVE  FORCE  AND  ENERGY.   475 

Let  unit  'quantity  of  electricity  pass  through  a  cell  of 
infinitely  small  resistance;  then,  by  Joule's  law,  the  work 
done  by  the  current  is  equal  to  E,  the  electromotive  force. 
But  e  gram  of  one  of  the  elements  of  the  electrolyte  has 
been  electrolysed,  in  accordance  with  Faraday's  law.  Let  6 
be  the  quantity  of  heat  developed  by  the  combination  of  one 
gram  of  this  element  to  reproduce  the  electrolyte,  then,  ac- 
cording to  Thomson,  since  no  work  is  expended  in  any  other 
part  of  the  circuit, 

E  =  JeO,  and  therefore  0  =  -^  . 

To  realise  this  equation  in  practice  a  great  many  corrections 
have  to  be  applied. 

This  formula  presents  us  with  an  electrical  method  for 
determining  the  heats  of  combination  of  various  elements,  or, 
we  may  say,  the  energy-changes  attending  the  formation  of 
various  compounds.  In  Joule's  papers,  the  values  of  the 
quantity  6  were  regarded  as  affording  measures  of  'the  in- 
tensities of  affinity '  of  different  substances  (loc.  cit.  20.  99) ; 
but  we  have  seen  that  this  cannot  now  be  held,  except  the 
term  '  affinity  '  is  used  in  a  very  vague  sense. 

Many  investigations  have  been  made  into  the  accuracy  of 
Thomson's  law  ;  but  I  cannot  attempt  to  trace  these  here. 
Some  results  shew  great  discrepancies  between  the  observed 
E.  M.  F.'s  of  cells  and  those  calculated  from  thermal  measure- 
ments of  the  chemical  changes  which  are  supposed  to  occur 
in  the  cells ;  but  unless  the  exact  chemical  changes  which 
occur  are  completely  known,  the  discrepancies  may  be  more 
fanciful  than  real1. 

Concluding  Remarks. 

249        We  have  thus  tried  to  gain  some  answers  to  the  questions 
with  which  we  started,  What  is  the  composition  of  compounds? 

1  Among  the  more  important  researches  may  be  mentioned ; — Braun,  Wied. 
Ann.  16,  561 ;  17.  593;  Wright,  Phil.  Mag.  (5)  9.  237,  331 ;  11.  169,  261,  348; 
13.  265  ;  14.  1 88;  16.  25 ;  a  general  account  of  his  work  to  the  end  of  1880  is 
given  by  Wright  in  Chem.  Naus,  42.  249 ;  see  also  Proc.  of  the  Physical  Society.  In 
connexion  with  Wright's  work,  see  Laurie's  criticism,  Phil.  Mag.,  August,  1886. 
See  also  B.  A.  'Reports  of  the  Electrolysis  Committee?  1886-88. 


4/6  CONCLUDING  REMARKS.  [BOOK  II. 

What  actions  are  compounds  capable  of  performing  ?  A 
complete  answer  to  either  question  will  be  an  answer  to  both, 
and  that  answer  will  include  the  whole  of  chemistry. 

The  atom  of  the  chemical  element  has  been  the  unit  with 
which  we  have  had  to  deal ;  the  properties  of  compounds  have 
been  regarded  as  conditioned  on  the  one  hand  by  the  nature, 
the  number,  and  the  arrangement,  of  the  elementary  atoms 
which  together  form  the  compound  molecules,  and  on  the  other 
hand,  by  the  greater  or  smaller  quantities  of  available  energy 
associated  with  these  molecules.  To  determine  the  relations 
between  the  properties  of  various  molecules,  and  the  nature, 
number,  and  arrangement,  of  their  constituent  atoms  was  the 
first  part  of  our  task ;  to  attempt  an  outline  of  a  dynamical 
explanation  of  chemical  operations  between  molecules  was 
the  object  of  the  second  part  of  the  undertaking. 

But  inasmuch  as  the  properties  which  chiefly  concern  us  as 
chemists  are  the  properties,  not  of  individual  substances,  but 
rather  of  these  considered  as  members  of  changing  systems,  it 
has  been  impossible  to  consider  the  questions  arising  in  the 
first  part  without  to  a  great  extent  making  use  of  methods 
and  conceptions  more  strictly  belonging  to  the  second  part 
of  our  subject. 

The  facts  connoted  by  the  expression  chemical  statics  were 
to  some  extent  classified  by  the  help  of  the  hypothesis  of 
valency,  itself  an  outcome  of  the  application  of  the  molecular 
and  atomic  theory  to  chemical  phenomena,  and  by  the  hypo- 
thesis regarding  the  relations  between  the  atomic  weights  of 
the  elements  and  the  properties  of  these  elements  and  their 
compounds  which  is  known  as  the  periodic  law.  The  deter- 
mination of  physical  constants,  and  more  particularly  the 
quantities  of  heat  which  are  produced  or  disappear  during 
chemical  changes,  the  refraction-equivalents,  the  specific  rota- 
tory powers,  and  the  relative  volumes,  of  typical  compounds 
and  classes  of  compounds,  helped  somewhat  towards  a  defi- 
nite knowledge  of  the  composition  of  these  compounds. 

The  study  of  chemical  kinetics,  we  found,  was  much 
advanced  by  the  dynamical  hypothesis  of  Guldberg  and 
Waage,  concerning  mass-action  and  chemical  affinity,  which 


CH.  III.  §249]  CONCLUDING   REMARKS.  477 

in  its  primary  form  is  nearly  independent  of  any  molecular 
theory  of  the  structure  of  matter,  but  in  its  development  and 
application  by  Ostwald  forms  a  bridge  connecting  the  in- 
vestigation of  the  chemical  properties  of  molecules  with  that 
of  the  actions  of  the  forces  which  come  into  play  during 
chemical  operations.  In  the  later  outcome  of  the  work  on 
affinity,  we  found  a  general  theory  of  chemical  change  be- 
tween electrolytes  in  solution.  Whether  we  accept  this  theory 
or  not,  we  must  admit  that  it  has  been  prolific  in  work  of 
first-class  importance.  It  has  advanced  our  conception  of 
chemical  change :  it  has  given  us  definite  measurements  of 
the  affinities  of  very  many  acids,  and  in  these  numbers  it  has 
presented  us  with  quantitative  connexions  between  the  con- 
stitutions, and  the  reactions,  of  those  acids. 

We  are  getting  nearer  the  goal  towards  which  chemists 
have  ever  striven  ;  we  are  learning  to  recognise  and  formulate 
definite  connexions  between  properties  and  composition. 

I  have  tried  always  to  exhibit  the  hypotheses  of  chemistry 
as  at  once  arising  from  facts,  and  serving  as  guides  in  the 
quest  for  facts  It  is  especially  necessary  to  do  this,  I  think, 
in  dealing  with  the  questions  concerning  structural  formulae. 
If  these  formulae  are  dissociated  from  the  chemical  facts  which 
they  symbolise  they  become  intellectual  tyrants;  if  each 
formula  is  considered  simply  as  a  summary  of  facts  regarding 
the  compound  formulated,  they  are  to  be  classed  with  the 
other  '  brute  beasts  of  the  intellectual  domain,'  and  cease  to 
have  much  interest  for  one  who  believes  that  chemistry  is  a 
branch  of  science. 

One  great  difficulty  in  using  chemical  hypotheses  consists 
in  determining  the  limits  of  the  class  of  phenomena  to  which 
each  hypothesis  may  be  applied.  Berzelius  carried  the  hypo- 
thesis of  dualism  too  far,  and  it  was  destroyed  by  the  more 
elastic  hypothesis  of  substitution  ;  in  our  own  day  the  hypo- 
thesis of  valency  has  frequently  been  applied  to  phenomena 
with  which  it  has  little  or  nothing  to  do. 

But  each  failure  to  explain  all  in  terms  of  one  hypothesis 
makes  us  more  hopeful  for  the  future,  and  convinces  us  that 


4/8  CONCLUDING   REMARKS.  [BOOK  II. 

we  have  to  deal  with  a  living  and  growing  part  of  the  study 
of  nature.     And  nature  is  finer  than  our  finest  analysis. 

Much  work  has  yet  to  be  done  before  a  general  theory  of 
chemical  change  can  be  hoped  for;  a  theory  which  shall 
represent  every  process  of  change  as  a  function  of  the  atomic 
weights  of  the  elements,  and  the  affinities  of  the  reacting 
substances  concerned  in  the  operation.  When  such  a  theory 
is  attained,  will  chemistry  be  complete  ?  I  hope  not ;  for 

'What's  come  to  perfection  perishes.' 


INDEX. 


The  numbers  refer  to  pages. 


ABNORMAL  VAPOUR  densities,  so  call- 
ed, 391 

Absorption-spectra       and       molecular 
structure,  connexion  between,  314 

Acetic  acid,  density  of  vapour  of,  203, 390 

Acids,  action  of  metals  on,  100,  264 
,,      affinities,  relative,  of,  413,  421, 

436,  439 

,,      classification  of,  by  help  of  ther- 
mal data,  269 

,,      Davy's  and  Dulong's  views   re- 
garding, 116 

,,      electrolysis  of,  422,  436,  443 
,,       Lavoisier's  views  regarding,  116 
,,       Liebig's  views  regarding,  117 
Additive,  cumulative,  constitutive, mean- 
ing of  terms,  456,  468 
Affinity,  a  unit  of,  use  of  expression  in 
hypothesis  of  valency,  132,134 
,,          and  valency  ought  not   to  be 

confused,  470 

,,         Berthollet's  work  on,  342 
,,         Berzelius' conception  of,  1 1 3 
,,        coefficients   of,   348,    378,  409 

et  seq.,  439  et  seq.,  463 
,,        connexions  between,  and  con- 
stitution, 439  et  seq. 
,,        connexions  between,  and  chan- 
ges of  energy,  279,  471 
,,        general  meaning  of  term,  340 
,,        not   to  be   identified  with  po- 
tential energy,  473 

,,        of    acids,  connexions  between 
and   conductivities    of  same 
acids,  422  et  seq.,  434,  443 
,,        Ostwald's  work  on,  408  et  seq., 

4&etuf. 

„        tables  of,  341,  440—445 
,,        'the  carbon  atom  has  four  units 

of,'  133 
,,        thermally  considered,  368,  410, 

4?i 
,,        Thomsen's   thermal   work  on, 

368,  410 
,,        use  of  term  by  older  chemists,  340 


Affinities,   relative,  of  acids,  413,  421, 

436,  439 

„  ,,  ,,  tables     of, 

421,  423,  440  et  seq. 
Alchemy,  the  conceptions  underlying,  2 
Allotropy,  142 

,,  experiments  by  Spring  bear- 

ing on,  142,  note 
,,  thermally  considered,  266 

Ammonium  carbamate,  dissociation  of, 

401 
,,  hydrosulphide,     „ 

400 

ARMSTRONG,  his  views  regarding  elec- 
trolysis, 465 
ARRHENIUS,  his  work  on   electrolytic 

dissociation,  454  et  seq. 
Asymmetric  atoms  of  carbon,  304 
ATKINSON,    R.    W.,    his    experiments 
bearing  on  molecular  compounds,  219 
Atom,  Daltonian  definition  of,  9 

,,       definition  of,  obtained  by  apply- 
ing Avogadro's  law,  38 
,,       each,  has  a  definite  replacing 

value,  122 

,,       function  of  given,  dependent  on 

structureof molecule,  i6^etsey. 

,,       molecule,    and    equivalent,   the 

terms  contrasted,  24,  192 
, ,       of  phosphorus  is  trivalent,  mean- 
ing of  this  expression,  131 
Atoms  and  molecules,  distinction  be- 
tween, based  on  reactions,  106 
,,       arrangement    of,  in   molecules, 

138  note,  154  note 

,,  classification  of,  by  their  valen- 
cies, 127 

, ,       double,  use  of  by  Berzelius,  20 
,,       equivalency  of  (see  also  valency), 

121  et  seq. 

,,  formula  for  finding  maximum 
number  of  monovalent,  in  a 
molecule,  144 

,,  valency  of  (see  also  valency), 
"5.  "9 


480 


INDEX. 


Atoms,   valency   of,   in    non-gasifiable 

compounds,  137,  242 
Atomic  heat  of  elements,  49,  60 
,,         refractions  of  elements,  292 
,,  ,,          of  carbon  and  oxy- 

gen, 298 

,,       synthesis,  Berzelian  rules  of,  18 
,,  ,,  Daltonian     ,,  9 

,,       theory,    shortcomings    of    the 

Daltonian,  1 1 
,,       volumes     of    elements,    curve 

shewing,  227 

,,       weight  of  an   element,  defini- 
tion of,  38 

„       weights,  Berzelius'  table  of,  19 
,,  „          data    required    before 

can  be  determined,38 
,,  ,,          determined   by  appli- 

cation of  Avogadro's 
law,  and  of  law  of 
Dulongand  Petit,  65 
,,  ,,          determined   by   appli- 

cation of  Mitscher- 
lich's  law  of  isomor- 
phism, 74 

„  „          determined  by  chemi- 

cal methods,  78 

„  ,,          of     beryllium,     tellu- 

rium, and  uranium, 
determined  by  ap- 
plication of  periodic 
law,  232 

,,  „          of  elements,  connexion 

between,  and   heats 
of  formation  of  ha- 
loid salts,  229 
,,  „          of  elements,  data  for, 

tables,  39,  86 

,,  „          of  elements,   periodic 

connexion  between, 

and     properties     of 

elements,  223  et  seq. 

,,  ,,          of  elements,  table  of, 

48 
Atomicity  of  molecules,  explanation  of 

term,  45 
,,  ,,  table  shewing, 

Avidity,  meaning  of  term  as   used  by 

Thomsen,  412 

AVOGADRO,  application  of  his  law  to 
determine  atomic  weights, 
compared  with  applica- 
tion of  law  of  Dulong  and 
Petit,  65 
„  his  distinction  between 

atom  and  molecule,  1 3 
,,  his  law,  13,  27 

„  „          accepted    by    Du- 

mas, 20 


AVOGADRO,  his  law  applied  to  chem- 
ical reactions,  29 

„  ,,  leads  to  definition 

of  atomic  weight, 

„  „  made  basis  of  sys- 

tem of  Gerhardt 
and  Laurent,  24 
„  ,,         not    accepted    by 

Berzelius,  7 

Axially  symmetric  molecules,  use  of 
term,  184 

BASE,  division  of  a,  between  two  acids, 
368,  37^ 

Bases,  classification  of,  by  help  of  ther- 
mal data,  272 

BEMMELEN,  VAN,  his  experiments  bear- 
ing on  molecular  compounds,  215 

BERGMANN,  his  tables  of  affinity,  341 
,,  his    work     in    connexion 

with  the  atomic  theory,  7 

BERTHELOT,  his  law  of  maximum  work, 

279'  383 

„  his  three  principles  of  ther- 

mal chemistry,  278 

BERTHOLLET,  his  study  of  affinity,  342 
,,  his      views      regarding 

chemical  change,  345 
,,  his  views  regarding  solu- 

tion, 343 

Beryllium,  atomic  weight  of,  232 
,,          fusibility  of  salts  of,  227 
,,          specific  heat  of,  62 
BERZELIUS,  his  acceptance  but  limita- 
tion of  Gay-Lussac's  law, 

17 

,,  his  electro-chemical  investi- 

gations, 113 

„  his  rules  with  regard  to 

atomic  synthesis,  18 

,,  his  table  of  atomic  weights, 

I9 

„  his  use   of  double  atoms, 

20 

,,  ,,  the  term  pola- 

rity, 114 

,,  his  work  on  atomic  synthe- 

sis, 17 
, ,  refuses  to  accept  Avogadro's 

law,  17 

,,  the  dualistic  theory  of,  115 

Boiling  points  of  carbon  compounds, 
connexions  between,  and  structure, 
286- 

Bonds,  free  and  satisfied,  132 
„      relative  strength  of,  198 
„      single,  double,  and  treble,  133, 

145 

„     saturation  of,  132 


INDEX. 


481 


Bonds,  Thomsen's   thermal    researches 

connected  with,  282 
„      use  of  term    in   hypothesis   of 

valency,  133  et  seq. 

Boron,  carbon,  and  silicon,  Kopp's  hy- 
pothesis regarding  atoms  of,  67 
,,       specific  heat  of,  63  et  seq. 
BRAUNER,  his  investigations  connected 

with  the  periodic  law,  234 
BRAUNER  and  WATTS,  their  work  on- 

specific  volumes,  325 
BRODIE,  his  work  bearing  on  structure 

of  small  particles  of  elements,  78 
Bromine,  relative  density  of  gaseous, 

203 

BRUHL,   his  work  on  the  refraction- 
equivalents  of  carbon  compounds,  291 
et  seq. 
BUNSEN,  his  work  on  mass-action,  346 

Calcium     carbonate,     dissociation     of, 

394 

CANNIZZARO,  his  generalisations  re- 
garding specific  heats  of  compounds, 
5* 

Capillarity-constants,  336 
Carbon,    boron,    and   silicon,     Kopp's 
hypothesis  regarding  atoms  of, 
67 

,,       specific  heat  of,  63 
Carbonyl  grouping  of  carbon  and  oxy- 
gen atoms,    meaning   of  expression, 
295 

CARNELLEY,  his  determinations  of  fusi- 
bility of  elements,  228 
,,  his  papers  on  the  periodic 

la\v,  230  note,  244  note 
CAYLEY,  his  mathematical  examination 

of  isomerism,  146  note 
Central  nucleus,  use  of  term,  168 
Chain,  closed,   open,  side,  meanings  of 

terms,  166 
Chemical  and  electrical  forces,  relations 

between,  474 

Chemical     change,     and    changes    of 
energy,        Berthollet's 
views  regarding,  345 
,,  Berzelius's    views    re- 

garding, 114 
„  considered        thermo- 

dynamically,  379 
,,  electrolytic  hypothesis 

of,  460 
,,  general  considerations 

regarding,  369 
„  influence  of  mass  on, 

339 

Chemical  changes  are  accompanied  by 
degradation  of  ener- 
gy, 27 
M.C. 


Chemical  changes  consist  of  two  parts, 

269,  296,  300 

,,  involving  degradation 

of  energy  usually  oc- 
cur, 259,  384 
Chemical  classification,  i,  121 

„         equilibrium,    hypotheses   re- 
garding, 363  et  seq. 
„         force,  use  of  term,  350,  355 
,,         methods      for      determining 
atomic    weights,    examples 
of,  78 

,,  methods  for  investigating  affi- 
nities of  the  acids,  409  et 
seq. 

,,  problems,  need  of  considering 
both  reacting  bodies  and 
forces  in,  5 

,,         Statics  and  Kinetics,  use  of 
these  terms  explained   and 
illustrated,  6,  339,  476 
Chemistry,  methods  by  which,  brought 
under  domain  of  dynamics, 
5 

„          thermal,  247  et  seq. 
„          the  fundamental  problem  of, 

4»  IJI»  373,  477 
,,          the  general  scope  of,  i 
,,          the    sphere    of,    contrasted 
with  spheres  of  dynamics 
and  physics,  4 
,,         the  two  lines  of  advance  in, 

i.  121,475 
Chlorine,  relative  density  of,  203 

„         specific  heat  of,  55 
CLARKE,    F.    W.,    his    investigations 
on   hydrated   and   dehydrated   salts, 

327 
Classification,  chemical,  based  on  theory 

of  types,  121 

,,  of  acids  and  bases  by  help 

of  thermal  data,    269  et 
seq. 

,,  of    elements      and    com- 

pounds by  help  of  ther- 
mal data,  266 

,,  of  elements  in  accordance 

with  their  atomic  heats, 
61 

„  of  elements  in  accordance 

with  the  periodic  law, 
235 

„  the  two  schemes  of,  adopt- 

ed in  chemistry,  r,  121 
CLAUSIUS,  his  molecular  hypothesis  of 

electrolysis,  385 

Closed  chain,  meaning  of  term,  166 
Coefficients  of  affinity,  409  et  seq.,  436 

,,         of  velocity,  355,  378 
Colloids  and  crystalloids,  215 

31 


482 


INDEX. 


Combining  weights  of  elements,  defini- 
tion of,  36 

„          weights  of  elements  do  not 
always  represent  equiva- 
lent weights,  16,  23 
Compound  radicles,  116,  119,  151 

„  ,,         possess  a   definite 

replacing  power, 
122 
Compounds,  atomic,  200 

„  classification  of,  by  help  of 

thermal  data,  267  etseq, 

,,  formulae   of  gaseous    and 

solid,  46,  137 
,,  isomorphism  of,  69 

„  molecular,  199  et  seq. 

„  specific  heats  of,  50,  54 

Conductivities  of  acids,  connexions  be- 
,,  tween,    and    affinities, 

422  et  seq.,  439  etseq. 
„  of  bases,  435 

Conductivity,  molecular,  424 
Constitution,  water  of,  326 
Constitutive  properties,  468 
COOKE,  J.  P.,  his  experiments  in  con- 
nexion with  physical  isomerism,  209 
Copper  sulphate,  dissociation  of,  396 
COUPER,  his  work  bearing  on  valency 

of  atoms,  123 
Crystalline  form,  determination  of,  as 

aid  in  fixing  atomic  weights,  69 
Crystallisation,  water  of,  326 
Ciimulative  properties,  468 

DALE  (see  GLADSTONE) 

DALTON,    development  of  the  atomic 

theory  of,  8 
,,         his  New  System  of  Chemical 

Philosophy,  9 
,,         his  reasons  for  giving  to  water 

the  formula  HO,  1 1 
,,         his   refusal   to   accept   Gay- 

Lussac's  law,  12 

,,         his  remarks  on  specific  heats  of 

solids,  liquids  and  gases,  48 

,,         his  rules   respecting   atomic 

synthesis,  10 
,,         shortcomings  of  his  atomic 

theory,  1 1 

DAVY,    his  electro-chemical  investiga- 
tions, 112 

,,       his  views  regarding  acids,  116 
Dilution,  influence  of,  on  conductivities 

of  acids,  424  et  seq. 
Dimorphism,  73 

Dissociation,  cases  of,  considered,  389 
,,  electrolytic,  454 

,,  meaning  of  term,  389 

,,  of    acetic    acid    vapour, 

39° 


Dissociation,  of  ammonium  carbamate, 

401 
,,  of    ammonium  hydrosul- 

phide,  400 

,,  of  calcium  carbonate,  394 

,,  of    compounds   of  silver 

chloride  with  ammonia, 
394 

of  copper  sulphate,  396 
of  hydrogen  iodide,  393 
of  iodine,  206 
of  saltsin  solution, 453,461 
of  sodium  phosphate,  397 
regarded  as   special  case 
of  chemical  equilibrium, 

399.  4°5 

,,  regarded  from  molecular 

theory    point    of   view, 
402 

,,  thermodynamically       re- 

garded, 403 
,,  treatment   of    by   Gibbs, 

402 
Divalent  atoms,  meaning  of  expression, 

126  et  seq. 

Divalent,  the  atom  of  tin  is,  in  given 
molecule,  but  is  tetravalent 
in  another  molecule,  128 
DIVERS,  his  experiments  on  the  action 

of  tin,  &c.,  on  nitric  acid,  109 
DONATH,  his  determination  of  the  spe- 
cific heat  of  uranium  oxide,  59 
Dualism,  opposed  by  Dumas,  118 

,,         opposed  to  Faraday's  electro- 
lytic laws,  117 
,,         system  of,  introduced  by  Ber- 

zelius,  115 

DULONG  and  PETIT,  their  law  regard- 
ing specific  heats  of  solid  elements, 
49,  60 

DUMAS,  his  early  acceptance  of  Avo- 
gadro's  law,  20 

,,        his  system  of  notation  partly 

atomic,  partly  equivalent,  21 

,,        introduces   the   conception  of 

types,  1 20  et  seq. 

„        opposes  the  dualistic  system  of 
Berzelius,  118 

Eka-aluminium,  eka-boron,  and  eka- 
silicon,  230 

Electro-chemical  investigations  of 
Arrhenius,  454 
Berzelius,  113 
Davy,  112 
Faraday,  117,  451 
Ostwald,  422  &c. 
Joule,  474 
Thomson,  475 

Electrolysis  of  acids,  422  et  seq. 


Electrolysis,  Faraday's  laws  of,  337 
Electrolytes,     action    of    solvents    on, 

465 

Electrolytic  dissociation,  hypothesis  of, 

Electrolytic    hypothesis     of    chemical 

change,  460 
Element,  the  old  conception  of,  i,  244 

note 
Elements,  atomic  heats  of,  49,  60 

,,         atomic  volumes,  curve  of,  227 
,,         atomic  weights  of,  data  for 
finding,  tables,  39  et  seq., 
86  et  seq. 

,,         atomic  weights  of,  table,  48 
,,         atoms  of,  have  definite  re- 
placing values,  122 
, ,         atoms  of,  valency  of  (see  also 
valency  of  atoms),   126  et 
seq. 
„         classification  of,   by  help  of 

thermal  data,  266 
,,         classification   of,    in  accord- 
ance   with     their    atomic 
heats,  6 1 

,,  classification  of,  in  accord- 
ance with  the  periodic  law, 
223  etseq. 

,,         fusibility  of,  228 
,,         isomorphism  of,  72 
,,         periodic  connexion  between 
atomic   weights  and   pro- 
perties of,  223  et  seq. 
,,         specific  heats  of,  law  of  Du- 
long  and  Petit  regarding, 
49,  60 

,,         specific  heats  of  some,  deter- 
mined indirectly,  54  et  seq, 
,,        specific  heats  of,  table,  51 
,,         study  of  properties  of,  by  help 

of  the  periodic  law,  232 
,,         unknown,  properties  of,  pre- 
dicted by  the  periodic  law, 
230 
Elementary  gases,  table   of  molecular 

weights  of,  33 

Endothermic  and  exothermic  changes, 
meaning  and  application  of  terms, 
252 

Energy-changes  accompanying  chemical 
changes,  176,  259, 
279,  384,  471 

,,  connected  with  affinity- 

changes,  471 

,,  measurements     of,    by 

electrical      methods, 

475 

,,  measurements    of,     by 

thermal        methods, 
250,  257,  288 


INDEX.  483 


Energy,  degradation  of,  accompanying 
chemical  changes,  259,  384, 
471 
,,        free  and  bound,  use  of  terms  by 

Helmholtz,  382 
Entropy,  379 
Equilibrium,  chemical,  363  et  seq. 

,,  ,,         equation  of,  349, 

374. 

,,  ,,         equation    of,    a- 

dapted   to   dif- 
ferent      cases, 

363..  374 

„  ,,         equation  of,  ap- 

plied  to  study 
of  affinity,  408 
et  seq. 
„  „         of  systems  of  four 

bodies,  367 

,,  „         molecular      me- 

thods    applied 
to,  385 

,,  „         thermal  methods 

applied  to,  368 

„  ,,         thermodynami- 

cal  methods  ap- 
plied to,  379 
Equilibrium-pressure,   use   of   term   in 

connexion  with  dissociation,  392 
Equivalency  of  atoms  (see  also  -valency), 

\  26  et  seq. 
Equivalent,  atom,  molecule,  the  terms 

contrasted,  24,  192 
,,          connected     with     function, 

J5»  23 
„          difficulty  of  determining  the 

true,  of  an  element,  14 
,,          notation,  inconveniences  of, 

,,          term    introduced    by    Wol- 

laston,  14 

,,          weights  of  elements  deter- 
mined by  Laurent,  23 
Equivalents,  work  of  Dumas,  Laurent, 

and  Gerhardt  on,  22 
Etherefication-values,     connexion    be- 
tween, and  molecu- 
lar structure  of  al- 
cohols, 331 
„  meaning  of  term,  332 

et  seq. 

Ethylene    grouping     of    two     carbon 
atoms,  meaning  of  expression,  295 


FARADAY,  his  electro-chemical  investi- 
gations, 117,  337 

FISCHER,  his  work  in  connexion  with 
the  atomic  theory,  7 

Fluorine,  specific  heat  of,  55 


484 


INDEX. 


Forms  of  oxides  and  salts  as  determined 
by  application  of  the  periodic  law, 

239 

Formulae,  chemical,  of  gases  compared 

*"  with  those  of  solids,  46 
„         chemical,  structural,  examples 
of  methods  of  obtaining, 
146  et  seq. 

„         chemical,  structural,  general- 
isations usually   made    in 
obtaining,  156  et  seq. 
FRANKLAND  recognises  a  substituting 

value  for  each  elementary  atom,  122 
Fusibility  of  elements,   connexion   be- 
tween, and  atomic  weights,  228 


Gallium,  identical  with  eka-alitminium, 

230 

GARNIER  and  CANNIZZARO,  their  gene- 
ralisation regarding  specific  heats  of 
compounds,  51  58 
Gases,  formulae  of,  compared  with  those 

of  solids,  46 
GAY-LUSSAC,  Berzelius  modifies  the  law 

of,  17 
,,  Dalton  refuses  to  accept 

the  law  of,  12 

,,  his   law   regarding  volu- 

metric combinations  of 
gases,  12 

Geometrical  isomerism,  182,  304,  445 
GERHARDT,  his  law  of  even  numbers, 

84,  198 

,,  his   reasons   for  changing 

the  equivalents  of  carbon, 
&c.,  22 
Germanium,  identical  with  eka-silicon, 

232 

GIBBS,  his  investigation  of  the  equili- 
brium of  heterogeneous  systems,  380, 
402 

GLADSTONE,hisinvestigalions  on  chemi- 
cal change,  347 

GLADSTONE  and  DALE,  their  investiga- 
tions   on     refraction-equivalents     of 
carbon-compounds,  291 
GLADSTONE  and  TRIBE,  their  investiga- 
tions in  connexion  with  the  electro- 
lysis of  acids,  100 
GMELIN,  his  system  of  notation,  21 
GOLDSTEIN,  his  investigations  on  the 
connexion  between  boiling  points  and 
molecular  structure,  286 
GRAHAM,  his   work  on  colloidal  and 

crystalloidal  matter,  214 
,,          his  work  on  water  of  crystal- 
lisation, 326 

GROTH,  his  investigations  regarding 
morfhotropic  relations,  173 


Group,  use  of  term  in  nomenclature   of 

the  periodic  law,  224 
GULDBERG  and  WAAGE, 

their  equation  of  chemical  equili- 
brium, 349,  374 

their  equation  of  chemical  equili- 
brium applied  to  study  of  chemical 
affinity,  408  et  seq. 

their  law  of  mass-action,  347  et 
seq. 

their  molecular  hypothesis.of  chemical 
equilibrium,  386 

Halogens,  hydracids  and  oxyacids  of, 

considered  thermally,  268 
HARTLEY,  his  investigation  of  relations 
of  molecular  structure  to  absorption- 
spectra,  314 

Heat,  connexion  between  quantities  of, 
produced  in  chemical  changes, 
and  structure   of  molecules  of 
changing  substances,  174  et  seq. 
,,     of  formation  of  compounds,  mean- 
ing of  term,  257  et  seq. 
,,     of  neutralisation  of  an  acid  by  a 

base,  and  vice  versa,  269,  368 
,,     produced    in  chemical    changes, 

study  of,  247  et  seq. 
,,     produced   in  reactions  of  isome- 

rides,  174,  282 

,,     specific,  of  solid  elements,  49,60 
(See    also    thermal   chemistry,    and 

thermal  data. ) 

HELMHOLTZ,   his  electro-chemical  in- 
vestigations, 382 
,,  his  use  of  the  terms  free 

and  bound  energy,  382 
,,  on  chemical  equilibrium, 

383 
HERMANN,  R.,  his  work  in  connexion 

with  specific  heats,  50 
HOFF,  J.  H.  VAN'T,  his  gravitational 
hypothesis       regarding 
atomic    valency,     135, 
note. 

„  his   hypothesis  regarding 

optically    active    com- 
pounds, 304  et  seq. 
„  his  law  of  osmotic  pres- 

sure, 452,  465 
,,  his    work    on     chemical 

equilibrium,  374,  384 
,,  his  work   on    velocity  of 

chemical  change,  360 
HOOD,  his  experiments  on  the  velocity 

of  chemical  change,  360 
HORSTMANN,  his  treatment  of  dissocia- 
tion-phenomena, 379 
HUMPIDGE,  on  spec,  heat  of  beryllium, 
63 


INDEX. 


485 


Hydrofluoric  acid,  density  of  vapour  of, 

126  note  (s.  Addenda). 
Hydrogen  iodide,  dissociation  of,  393 
Hydrogen,  replaceable,  illustrations  of, 

163  &c. 
,,          specific  heat  of,  56 

latro-chemists,  2 

Iodine,  atomic  weight  of,  fixed  by  help 

of  periodic  law,  233 
,,       relative  density  of  vapour  of, 

206 

Ions,  free,  in  solutions,  461 
ISAMBERT,  his  work  on  dissociation  of 

ammonium  hyclrosulphide,  400 
Isomerides,  formula  for  finding  maxi- 
mum  number   of  monad 
atoms  in  molecules  of,  144 
,,  heat  produced   or   used    in 

reactions  of,  174,282 
Isomerism,    detailed    consideration   of, 

143**?. 

,,  exceptions  to,  generally 
adopted  explanation  of, 
180 

geometrical,  182,  304,  445 
,,  hypothesis    by    which    ex- 

plained, [39,  181  . 
,,  mathematical    examination 


of,  by  Cay  ley,  146  note 
eaning  of  term, 


g  o   term,  139 
,,  thermally  considered,  174^ 

seq. 

,,  physical,  211 

,,  ,,         Lehmann's    work 

on,  210  et  seq, 

,,          position,  and  saturation,  294 
,,  study  of,  by  optical  methods, 

292  et  seq,  304,  311 
,,        .   study  of,    by  thermal   me- 

thods, 174  et  seq. 
Isomorphism  of  compounds,  69 
,,  of  elements,  72 

,,  Mitscherlich's  law  of,  69 

Isomorphous   crystals,  meaning   to   be 

given  to  this  expression,  71 
Isotonic  solutions,  452 

JOULE,  his  electro-chemical  investiga- 
tions, 474 

KANONNIKOW,  his  work  on  refraction- 

equivalents,  298  note 
KEKULE,  his  use  of  the  terms  atomic 
and  molecular  compounds, 
200 
KEKULE,  his  work  on  valency  of  atoms, 

123 

Kinetics,  chemical,  general  remarks  re- 
garding, 339 


Kinetics,  chemical,  use  of  term  explain- 
ed, 6 
KOHLRAUSCH,  his  law  of  electrolytic 

conductivity,  428 

KOPP,  his  hypothesis  regarding  the 
atoms  of  carbon,  boron,  and 
silicon,  67 

,,        his  investigations  regarding  spe- 
cificheatsof  elements,  $ietseq. 
,,        his  investigations  regarding  spe- 
cific •volumes,  319  et  seq. 

LANDOLT,  his  work  on  optical  activity 
of  carbon  compounds,  301 
et  seq. 
LAURENT,  his  definition  of  molecule 

and  atom,  24 
,,  his  system  based  on  Avo- 

gadro's  law,  24 
„  his  work  on    equivalents, 

23 
LAVOISIER,  his  views  regarding  acids, 

116 
Law,   Berthelot's,   of  maximum   work, 

279.  383 

,,  of  Avogadro  (see  also  AvOGAD- 
RO),  13,  27 

,,  of  dilution,  as  regards  conduc- 
tivity, 424  et  seq. 

,,     of  Dulong  and  Petit,  49,  60 

,,     of  Gay-Lussac    (see    also   GAY- 

LUSSAC),    12 

,,     of  Kohlrausch  regarding  electro- 
lytic conductivity,  428     ' 
,,     of  mass-action,  348 
„     of  molecular  lowering  of  freezing 

point,  76,  452 

,,     of  osmotic  pressure,  452 
,,     periodic  (see  also  periodic  law), 

222  et  seq. 

LflHM ANN,  his  work  on  molecular  com- 
pounds, 210 
„          his  work  on  physical  isomer- 

ism,  210  et  seq. 
LEMOINE,  his  studies  on  dissociation, 

393 

LIEBIG,  his  views  regarding  acids,  117 
Links,  or  bonds,  use   of  term,  in  hy- 
pothesis of  valency  (see  also  bonds), 

X33 

Long  and  short  periods,  235 
LOSSEN,  his  criticism  of  hypothesis  of 

bonds,  133,  193  et  seq. 
,,          his  investigations  in  connexion 
with  specific  volume  of  the 
group  CH2,  322 

,,          illustrations   of  his   views  re- 
garding valency,  145 

Magnetic  rotatory  power,  311 


486 


INDEX. 


MALLET,  his  determination  of  the  va- 
pour density  of  hydrofluoric 
acid,  126  note 

MARIGNAC,  his  work  on  the  supposed 
element  hyponiobium,  75 

Mass-action,  law  of,  348  et  seq. 

Maximum    work,    Berthelot's    law   of, 

279.  383 

MENDELEJEFF,  his  researches  in  con- 
nexion with  theperiodiclaw,  ii^etseq. 
MENSCHUTKIN'S  investigation  of  etheri- 
fication-values  of  alcohols  and  acids, 
331  et  seq. 
Metals,  action  of  acids  on,  100 

,,        action  of  acids  on,  considered 

thermally,  264 
Metamerism,  143 

,,         physical,  213 

MEYER,  L.,  his  calculation  of  the  spe- 
cific heat  of  beryllium,  63 
„  his  remarks  on  affinity,  471 

,,  his  work  in  connexion  with 

specific  volumes,  330 
,,  his  work  in  connexion  with 

the  periodic  law,  223  et 
seq. 

MITSCHERLICH,    his    law   of   isomor- 
phism, 69 

Molecular  compounds,  general  remarks 
on,   200,  207, 
219 
,,  ,,  Lehmann's  work 

on,  208 

,,  „  no  definition  of, 

possible,  200 
,,         conductivity,  424 
, ,         groups,  existence  of,  in  gases, 

203 

,,         heats    of  solid    compounds 
help  to  determine  atomic 
weights  of  elements,  54 
,,         heat    of    solid    compounds, 
meaning  of  expression,  54 
note 
,,         lowering  of  freezing   point, 

law  of,  76,  452 

,,         phenomena    dealt    with    by 
statistical  methods,  99  note 
,,         structure,  138,  154  note 
,,         structure,      connexion      be- 
tween,    and     absorption- 
spectra,  314 

,,         structure,      connexion      be- 
tween, and  affinity,  439 
,,         structure,  connexion  between, 
and  arrangement  of  atoms 
in  space,  182 

,,  structure,  connexion  between, 
and  etherification-values, 
331 


Molecular  structure,  connexions  be- 
tween, and  magnetic  ro- 
tatory power,  3 1 1  et  seq. 

, ,  structure,  connexion  between, 
and  optical  activity,  303 
et  seq. 

,,  structure,  connexionbetween, 
and  thermal  changes,  174 
et  seq.,  282 

,,  structure,  examples  of  de- 
pendence of  function  of 
part  of  a  molecule  on 
arrangement  of  all  the 
parts,  163  et  seq. 

,,  structure,  examples  of  pre- 
sence of  certain  atomic 
groups  in  molecules,  151 
et  seq. 

,,  theory,  general  sketch  of,  25 
et  seq. 

„         volumes,  317  et  seq. 

„  weight  of  a  gas,  definition  of, 
32 

,,  weight  of  a  gas,  examples 
shewing  how  determined, 
35 

,,  weight,  same  substance  may 
have  more  than  one,  35 

,,  weights  of  elementary  gases, 
table  of,  33 

,,  weights  of  substances  in  so- 
lution determined,  76,  456 
note 

Molecule,  atom,  equivalent,  the  terms 
contrasted,  24,  192 

,,         dynamical  conception  of,  26 

,,  physical,  compared  with  che- 
mical, conception  of, 
220 

Molecules  and  atoms,  distinction  be- 
tween, based  on  reac- 
tions, 1 06 

,,  atomicity  of  elementary, 
table,  45 

,,  attempts  to  measure  ther- 
mal changes  accompany- 
ing separation  of,  into 
atoms,  263 

,,  in  which  isomerism  may 
occur,  146 

,,  of  hydrogen,  &c.,  separate 
into  parts  during  chemical 
changes,  29 

,,  saturated  and  unsaturated, 
use  of  terms,  145 

,,         size  of,  28 

Monovalent  atoms,  formula  for  finding 
maximum  number  of,  in  a  molecule, 

M4 
Monovalent,  meaning  of  term,  126 


INDEX. 


487 


Morphotropic  relations,  use  of  expres- 
sion by  Groth,  173 

Nascent  actions,  examples  of,  97 

,,  „        explanation   of,  given 

by    the     molecular 
theory,  98 

,,  ,,        general    remarks    on 

use   of  the  expres- 
sion, 109 
,,  ,,        Traube's  experiments 

on,  106 

,,       state  of  compounds,  99 
NASINI,  his   work  on  refraction-equi- 
valents, 298 
NEUMANN,  his  extension  of  the  law  of 

Dulong  and  Petit,  50 
NEWLANDS,   his    work    in    connexion . 

with  the  periodic  law,  223 
NILSON  and  PETTERSSON,  their  deter- 
mination of  the  specific  heat  of  beryl- 
lium, 62 

NILSON  and  PETTERSSON,  their  work  in 
connexion  with  the  periodic  law,  233 
Nitrogen,  specific  heat  of,  55 

.  ,,         tetroxide,     relative     density 

of,  203 
Nucleus,  central,  meaning  of  term,  168 

Odd  and  even  series,  237 

ODLING   introduces   notation   shewing 

valencies  of  elementary  atoms,  122 
Open  chain,  meaning  of  term,  166 
Optically  active   compounds,  meaning 

of  expression,  299 

Optically  active  compounds,  van't 
Hoff's  hypothesis  concerning,  304 
et  seq. 

Optical   activity,  influence  of  inactive 

solvents  on,  301,  310 

,,  ,,         of  solid  compounds, 

302 
Optical   methods   applied  to  questions 

of  chemical  statics,  289  et  seq. 
Osmotic  pressures,  451 
OSTWALD,    his  application  of  law  of 
mass-action   to    dissoci- 
ation, 399 

,,  his  notation  used  in  ther- 

mal chemistry,  251 
,,  his    work    on    affinity-co- 

efficients  of    acids    and 
bases,  409  et  seq. 

„  his  work  on  conductivities 

and    affinities   of  acids, 
422  et  seq.,  460 

,,  his  work    on    connexions 

between     affinities    and 
constitution  of  acids,  439 


OSTWALD,  his  work  on  distribution  of 
a  base  between  two  acids, 

353>  372 
Oxygen,    atomic    weight  of,    data  for 

determining,  38 

,,          in  oxides,  specific  heat  of,  58 
,,         specific  heat  of,  56 

Periodic  law,  applied  to  predict  proper- 
ties of  unknown  ele- 
ments, 230 

„  applied  to  study  of  forms 

of    oxides    and    salts, 
239 

,,  applied  to  study  of  pro- 

perties    of    beryllium, 
232 

,,  applied  to  study  of  pro- 

perties of  known  ele- 
ments, 232  et  seq. 
„  applied  to  study  of  pro- 

perties of  uranium,  234 
,,  applied  to  study  of  valen- 

cies     of      elementary 
atoms,  241 

general  remarks  on,  244 
illustrations  of,  2  24  et  seq. 
nomenclature    employed, 

224,  230,  237 
statement  of,  223 
tables   shewing    arrange- 
ment   of    elements    in 
accordance  with,   225, 
236 

Periods,  long,  short,  and  transition,  use 
of  terms  in  nomenclature  of  the 
periodic  law,  235 

PERKIN,  on  the  connexions  between 
molecular  structure  and  magnetic  ro- 
tation, 3 1 1  il  seq. 

PETIT  and  DULONG,  their  law  regard- 
ing specific  heats  of  solid  elements, 
49,  60 

PETTERSSON  (see  NILSON) 
PFAUNDLER,  his  hypothesis  regarding 
chemical     equilibrium, 
386 

Phosphorus,  change  from  yellow  to  red, 
a  case  of  chemical  equi- 
librium, 366 

, ,  pentachloride,  relative  den- 

sity of  vapour  of,  202 
Physical  methods  applied  to  questions 

of  chemical  statics,  246  et  seq. 
PICKERING,  his  examination  of  the  ac- 
tion   of   sulphuric   acid    on  copper, 

94 
Plane-symmetric  molecules,  use  of  term , 

184 
Polarity,  use  of  term  by  Berzelius,  114 


INDEX. 


Polymerism,  141 

,,  physical,  213 

Polymorphism,  73 

POTILITZIN,  his  experiments  on  in- 
fluence of  mass  in  chemical  changes, 
276 

Radicles,  compound,  116,  119,  151 
,,  ,,  possess  a  definite 

replacing  power, 
122 

RAMSAY,  his  experiments  in  connexion 
with  specific  volumes,  320 

RAMSAY  and  YOUNG,  their  experi- 
ments on  vapour  density  of  acetic 
acid,  390 

RAOULT,  his  law  of  molecular  lowering 
of  freezing-points,  76,  452 

RATHKE,  on  molecular  compounds,  201 

Refraction-equivalent  of  a  compound, 
is  it  equal  to  sum  of  equivalents  of 
elementary  constituents?  292  et  seq. 

Refraction-equivalent,  meaning  of  term, 

Refraction-equivalents,  connexion  be- 
tween and  structure  of  carbon  com- 
pounds, 291  et  seq, 

Refraction-equivalents,  formulae  for  de- 
termining, 290 
,,  of     elementary 

atoms,  295 

,,  of   solid    com- 

pounds,  298 
note 
REGNAULT,  his  researches  on  specific 

heat,  50 
REYNOLDS,  R.  E.,   his   determination 

of  the  specific  heat  of  beryllium,  62 
RICHTER,  his  work  in  connexion  with 

the  atomic  theory,  7 
ROSE,  H. ,  his  supposed  discovery  of  an 

allotropic  form  of  niobium,  75 
Rotatory  power,  specific,  determination 

of,  300 

„  specific,  meaning  of  ex- 

pression, 300 

Saturated  and  unsaturated  molecules, 

use  of  terms,  145 

Scandium,  identical  with  eka-boron,  231 
SCHIFF,  his   work   in  connexion  with 

specific  volumes,  320 
Series,  use  of  term  in  nomenclature  of 

the  periodic  law,  237 
Side  chain,  meaning  of  term,  166 
Silicon,  carbon,  and  boron,  Kopp's  hy- 
pothesis regarding  atoms  of,  67 
,,       specific  heat  of,  63 
Silver    chloride,    compounds    of   with 

ammonia,  dissociation  of,  394 


Sodium  phosphate,  dissociation  of,  397 
Solution,  Berthollet's  views  regarding, 

37° 
Specific  heat  of  beryllium,  62 

,,         ,,         boron,      carbon,      and 

silicon,  63 

,,         ,,         oxygen  in  oxides,  58 
Specific  heats  of  compounds,  generalisa- 
tion of  Gamier  and 
Cannizzaro      regard- 
ing. 5i 

,,  ,,  of  compounds,  generalisa- 
tion of  Neumann  re- 
garding, 50 

,,  ,,  of  elements,  law  of  Du- 
long  and  Petit  re- 
garding, 49,  60 

,,         ,,     of  elements,  table,  51  etseq. 
,,         ,,     of  some  elements  determin- 
ed indirectly,  Betsey. 
Specific  refractive  energy,  meaning  of 

expression,  290 
,,         rotatory  power,  determination 

of,  300 
,,         rotatory    power,   meaning    of 

expression,  300 
,,         unipolarity,  use  of  expression 

by  Berzelius,  114 

, ,  volume  of  a  compound  proba- 
bly equal  to  sum  of  volumes 
of  elementary  constituents, 
3^9'  3^8 

,,  volume  of  carbon  and  of  oxy- 
gen varies  according  to  the 
valency  of  the  atom  of  each 
element,  319  et  seq. 
,,  volume,  meaning  of  expres- 
sion, 317 

,,  volumes  of  atoms  in  molecules 
vary  according  to  distribu- 
tion of  interatomic  reac- 
tions, 322 

,,         volumes  of  hydrated  and  de- 
hydrated salts,  327 
,,         volumes  of  solid  compounds, 

325 
SPRING,  his  experiments  in  connexion 

with  allotropy,  142  note. 
Stability, vagueness  of  theterm,  178,  465 
ST^DEL,   his    experiments   on  specific 

volumes  of  carbon  compounds,  323 
Statics,  chemical,  questions  of,  studied 

by  physical  methods,  246 
,,       chemical,  use  of  expression,  ex- 
plained and  illustrated,  6,  329 

Tables  of  affinity,  341,  440 — 445 
Table,  atomic  weights  of  elements,  48 
,,      atomic  weights  of  elements,  data, 
39,  86 


INDEX. 


489 


Table,  atomicity  of  elementary   mole- 
cules, 45 
,,       data  for  finding  maximum  atomic 

weight  of  oxygen,  36 
,,       illustrating    electrical    conduc- 
tivities and  velocity-constants 
of  acids,  423 

„  illustrating  law  of  dilution  as 
regards  conductivities  of 
acids,  425 

,,       illustrating     saponification  -  ve- 
locities and    electrical    con- 
ductivities of  bases,  436 
,,       molecular  weights  of  element- 
ary gases,  33 

,,       periodic    arrangement   of    ele- 
ments, 225,  236 
,,       relative  affinities  of  the  acids, 

440—445 

,,  relative  densities  of  halogens, 
nitrogen  tetroxide,  and  phos- 
phorus pentachloride,  202, 
203,  206,  207 

,,       specific  heats  of  elements,  51 
,,       thermo-atomic    weights    (Reg- 

nault),  50 
Tellurium,  atomic  weight  of,  fixed  by 

application  of  the  periodic  law,  233 
Thermal  chemistry,  attempts  made  in, 
to  distinguish  between  the 
two   parts    of   a    chemical 
change,  248,  262,  275 
„        chemistry,    Berthelot's     three 

principles  of,  278 

,,  chemistry,  illustrations  of  me- 
thods of  calculation  used  in, 
255  et  seq. 

,,        chemistry,  need  of  considering 
action  of  excess  of  reacting 
substances  in,  276 
„        chemistry,  need  of  considering 
physical  conditions  of  chang- 
ing systems  in,  275,  277 
,,        chemistry,    notation   used   in, 

248,  251 
„        chemistry,  principles  on  which 

based,  247 

,,        chemistry,    the  law  of  maxi- 
mum work  in,  279,  383 
„        data,  applied  to  action  of  acids 

on  metals,  264  et  seq. 
„        data,  applied  to  action  of  con- 
centrated and  dilute  hydri- 
odic  acid,  253,  260 
,,        data,  applied  to  action  of  sul- 
phuretted hydrogen  on  me- 
tallic salts,  260  et  seq. 
„        data,  applied  to  allotropy,  266 
,,        data,  applied  to  classification 
of  acids  and  bases,  269  et  seq. 

M.  C. 


Thermal  data,  applied  to  classification 

of  compounds,  268  et  seq. 
„        data,  applied  to  classification 

of  elements,  266 

,,        data,  applied  to  study  of  affi- 
nity, 368,  410,  471 
„        data,  applied  to  study  of  iso- 

merism,  1 74  et  seq. 
,,        data,  examples  of  attempts  to 

analyse,  277 
„        data,  influence  of  temperature 

on,  275 

,,        methods  used  in  chemistry,  247 
Thermodynamical  methods  applied  to 

chemical  equilibrium,  379 
THOMSEN,  J.,  his  attempt  to  measure 
the   thermal  value  of 
each  bond  of  the  car- 
bon atom,  282 

, ,  his  classification  of  acids 

and  bases,  based  on 
thermal  data,  269  et 
seq. 

,,  his  experiments  on  the 

connexions  between 
thermal  changes  and 
molecular  structure, 
174  et  seq.,  282 

,,  his  thermal  study  of  the 

affinities  of  acids,  368, 
410 

„  his  statement  of  the  law 

of  maximum  work,  280 
,,  his  use  of  the  term  avi- 

dity, 412 

„  his  work  on  division  of 

a  base  between  two 
acids,  368 

THOMSON,   J.    J.,    his    conception    of 

equilibrium  from  the  stand-point  of 

the  theory  of  vortex-atoms,  387,  403 

THOMSON,  Sir  W.,  his  electro-chemical 

investigations,  475 

THORPE,  his  experiments  on   relative 
density  of  hydrofluoric  acid 
gas,  126  note  (s.  Addenda) 
,,         his  investigations  in  connex- 
ion with  specific   volumes, 

323 

,,        his  investigations  of  the  re- 
ducing action  of  metals  on 
ferric  sulphate,  105 
,,         andWATTS,  their  experiments 
in  connexion  with  water  of 
crystallisation,  327 
TOMMASI,  his  work  in  connexion  with 

nascent  actions,  105 
Transition-periods,  use  of  expression  in 
nomenclature  of  the  periodic  law,  235 
Transpiration-rates,  336 

32 


490 


INDEX. 


TRAUBE,  his  experiments  in  connexion 
with  nascent  actions,  106 

TRIBE  (see  GLADSTONE) 

Trimorphism,  73 

TROOST  and  HAUTEFEUILLE,  their  ex- 
amination of  change  of  yellow  to  red 
phosphorus,  366 

Types,  classification  based  on,  120 
„       conception    of,    introduced    by 
Dumas,  118  et  seq. 

Typical  elements,  use  of  expression  in 
nomenclature  of  the  periodic  law,  237 

Uranium,  atomic  weight  of,  fixed  by 
application  of  the  periodic 
law,  234 
,,        specific  heat  of,  59 

Valency,    a,   use   of   expression,    132, 

136  note 

Valency  of  atoms,  conception  of,  applied 
to  explain  molecular 
structure,  154  et  seq. 

,,  conception  of,  applied 

to  finding  best  struc- 
tural formula  for  a 
given  compound,  144 
et  seq. 

,,  data   for   determining, 

127 

,,  definition  of,  129 

,,  discussion  of  notation 

adopted  in  hypothe- 
sis of,  132  et  seq. 

,,  geometrical  notion  re- 

garding, 182 

,,  gravitational  notion  of 

van't  Hoft,  135  note 

,,  in  non-gasifiable  com- 

pounds, 137,  241 

,,  limitations     made     in 

applying  the  concep- 
tion of,  154 

,,  Lossen's  views  regard- 

ing, 145,  193  et  seq. 

, ,  meaning  of  expression, 

I3l 

,,  ought   not   to  be  con- 

founded with  affinity, 
470 

,,  probably  varies  period- 

ically with  relative 
weights  of  the  atoms, 
241 

Vapour  densities,  bearings  of  dissocia- 
tion on  determina- 
tions of,  391 


Vapour  densities,  definition  of  expres- 
sion, 34  note 

,,  methods  of   determin- 

ing. 35  note 

,,  must  be  supplemented 

by    analyses     before 
molecular  weights  of 
compounds    can    be 
found  by  means  of,  35 
Velocities    of    chemical    actions,    con- 
nexion between,  and  affinities  of  re- 
acting substances,  356  et  seq. 
Volume,  atomic,  of  elements,  curve  of, 

227 

,,        specific,    meaning   of   expres- 
sion, 317 

Volumetric  methods  of  studying  chemi- 
cal operations  adopted  by  Ost  wald,  372 
Vortex  atoms,  bearing  of  theory  of,  on 
chemical  equilibrium,  387,  403 

WAAGE  (see  GULDBERG) 
WARDER,  his  experiments  on  the  af- 
finities of  bases,  360 
Water,  basic  and  saline,  326 

,,       effect  of  traces  of,  in  chemical 

changes,  467 
„       of  constitution,  327 
,,       of  crystallisation,  328 
WATTS  (see  BRAUNER,  also  THORPE 
WEBER,  his  determinations  of  the  spc 
cific  heats  of  boron,  carbon,  and  sil 
con,  63 

WIEDEMANN,  E.,  his  attempt  to  mec 
sure   heat  used  in  separating  mol< 
cule  of  hydrogen  into  atoms,  263 
WILLIAMSON,  his  hypothesis  regardin 
chemical  equilibriun  . 
385 
,,  his    researches    on    thv 

ethers,  80 

WITT,  his  experiments  on  the  connex- 
ion between  molecular  structure  and 
tinctorial  properties,  172 
WOLLASTON,  introduces  the  use  of  the 

term  equivalent,  14 
,,  objections  to  his  method 

of  determining  equiva- 
lents, ty 

YOUNG  (see  RAMSAY). 

ZANDER,  his  experiments  on  specific 
volumes  of  carbon  compounds,  322 

ZIMMERMANN,  his  determination  of  the 
specific  heat  of  uranium,  59 


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